Modular Group : Gamma(N)
The group Gamma(N) is the set of matrices in SL2Z
which is congruent to I modulo N.
| N | Genus |
Dimension of the Space of Modular Forms of Specific Weight |
|---|
| Weight 0 |
Weight 2 | Weight 4 | Weight 6 |
Weight 8 | Weight 10 | Weight 12 |
Weight 14 | Weight 16 |
Weight 18 | Weight 20 |
| 2 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 3 | 0 | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 |
| 4 | 0 | 1 | 5 | 9 | 13 | 17 | 21 | 25 | 29 | 33 | 37 | 41 |
| 5 | 0 | 1 | 11 | 21 | 31 | 41 | 51 | 61 | 71 | 81 | 91 | 101 |
| 6 | 1 | 1 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 |
| 7 | 3 | 1 | 26 | 54 | 82 | 110 | 138 | 166 | 194 | 222 | 250 | 278 |
| 8 | 5 | 1 | 28 | 60 | 92 | 124 | 156 | 188 | 220 | 252 | 284 | 316 |
| 9 | 10 | 1 | 45 | 99 | 153 | 207 | 261 | 315 | 369 | 423 | 477 | 531 |
| 10 | 13 | 1 | 48 | 108 | 168 | 228 | 288 | 348 | 408 | 468 | 528 | 588 |
| 11 | 26 | 1 | 85 | 195 | 305 | 415 | 525 | 635 | 745 | 855 | 965 | 1075 |
| 12 | 25 | 1 | 72 | 168 | 264 | 360 | 456 | 552 | 648 | 744 | 840 | 936 |
| 13 | 50 | 1 | 133 | 315 | 497 | 679 | 861 | 1043 | 1225 | 1407 | 1589 | 1771 |
| 14 | 49 | 1 | 120 | 288 | 456 | 624 | 792 | 960 | 1128 | 1296 | 1464 | 1632 |
| 15 | 73 | 1 | 168 | 408 | 648 | 888 | 1128 | 1368 | 1608 | 1848 | 2088 | 2328 |
| 16 | 81 | 1 | 176 | 432 | 688 | 944 | 1200 | 1456 | 1712 | 1968 | 2224 | 2480 |
| 17 | 133 | 1 | 276 | 684 | 1092 | 1500 | 1908 | 2316 | 2724 | 3132 | 3540 | 3948 |
| 18 | 109 | 1 | 216 | 540 | 864 | 1188 | 1512 | 1836 | 2160 | 2484 | 2808 | 3132 |
| 19 | 196 | 1 | 375 | 945 | 1515 | 2085 | 2655 | 3225 | 3795 | 4365 | 4935 | 5505 |
| 20 | 169 | 1 | 312 | 792 | 1272 | 1752 | 2232 | 2712 | 3192 | 3672 | 4152 | 4632 |
| 21 | 241 | 1 | 432 | 1104 | 1776 | 2448 | 3120 | 3792 | 4464 | 5136 | 5808 | 6480 |
| 22 | 241 | 1 | 420 | 1080 | 1740 | 2400 | 3060 | 3720 | 4380 | 5040 | 5700 | 6360 |
| 23 | 375 | 1 | 638 | 1650 | 2662 | 3674 | 4686 | 5698 | 6710 | 7722 | 8734 | 9746 |
| 24 | 289 | 1 | 480 | 1248 | 2016 | 2784 | 3552 | 4320 | 5088 | 5856 | 6624 | 7392 |
| 25 | 476 | 1 | 775 | 2025 | 3275 | 4525 | 5775 | 7025 | 8275 | 9525 | 10775 | 12025 |
| 26 | 421 | 1 | 672 | 1764 | 2856 | 3948 | 5040 | 6132 | 7224 | 8316 | 9408 | 10500 |
| 27 | 568 | 1 | 891 | 2349 | 3807 | 5265 | 6723 | 8181 | 9639 | 11097 | 12555 | 14013 |
| 28 | 529 | 1 | 816 | 2160 | 3504 | 4848 | 6192 | 7536 | 8880 | 10224 | 11568 | 12912 |
| 29 | 806 | 1 | 1225 | 3255 | 5285 | 7315 | 9345 | 11375 | 13405 | 15435 | 17465 | 19495 |
| 30 | 577 | 1 | 864 | 2304 | 3744 | 5184 | 6624 | 8064 | 9504 | 10944 | 12384 | 13824 |
| 31 | 1001 | 1 | 1480 | 3960 | 6440 | 8920 | 11400 | 13880 | 16360 | 18840 | 21320 | 23800 |
| 32 | 833 | 1 | 1216 | 3264 | 5312 | 7360 | 9408 | 11456 | 13504 | 15552 | 17600 | 19648 |
| 33 | 1081 | 1 | 1560 | 4200 | 6840 | 9480 | 12120 | 14760 | 17400 | 20040 | 22680 | 25320 |
| 34 | 1009 | 1 | 1440 | 3888 | 6336 | 8784 | 11232 | 13680 | 16128 | 18576 | 21024 | 23472 |
| 35 | 1393 | 1 | 1968 | 5328 | 8688 | 12048 | 15408 | 18768 | 22128 | 25488 | 28848 | 32208 |
| 36 | 1081 | 1 | 1512 | 4104 | 6696 | 9288 | 11880 | 14472 | 17064 | 19656 | 22248 | 24840 |
| 37 | 1768 | 1 | 2451 | 6669 | 10887 | 15105 | 19323 | 23541 | 27759 | 31977 | 36195 | 40413 |
| 38 | 1441 | 1 | 1980 | 5400 | 8820 | 12240 | 15660 | 19080 | 22500 | 25920 | 29340 | 32760 |
| 39 | 1849 | 1 | 2520 | 6888 | 11256 | 15624 | 19992 | 24360 | 28728 | 33096 | 37464 | 41832 |
| 40 | 1633 | 1 | 2208 | 6048 | 9888 | 13728 | 17568 | 21408 | 25248 | 29088 | 32928 | 36768 |
| 41 | 2451 | 1 | 3290 | 9030 | 14770 | 20510 | 26250 | 31990 | 37730 | 43470 | 49210 | 54950 |
| 42 | 1729 | 1 | 2304 | 6336 | 10368 | 14400 | 18432 | 22464 | 26496 | 30528 | 34560 | 38592 |
| 43 | 2850 | 1 | 3773 | 10395 | 17017 | 23639 | 30261 | 36883 | 43505 | 50127 | 56749 | 63371 |
| 44 | 2281 | 1 | 3000 | 8280 | 13560 | 18840 | 24120 | 29400 | 34680 | 39960 | 45240 | 50520 |
| 45 | 2809 | 1 | 3672 | 10152 | 16632 | 23112 | 29592 | 36072 | 42552 | 49032 | 55512 | 61992 |
| 46 | 2641 | 1 | 3432 | 9504 | 15576 | 21648 | 27720 | 33792 | 39864 | 45936 | 52008 | 58080 |
| 47 | 3773 | 1 | 4876 | 13524 | 22172 | 30820 | 39468 | 48116 | 56764 | 65412 | 74060 | 82708 |
| 48 | 2689 | 1 | 3456 | 9600 | 15744 | 21888 | 28032 | 34176 | 40320 | 46464 | 52608 | 58752 |
| 49 | 4215 | 1 | 5390 | 14994 | 24598 | 34202 | 43806 | 53410 | 63014 | 72618 | 82222 | 91826 |