↑

Properties

Label 4.15
Level 4
Weight 15
Dimension 6
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 15
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(4))\).

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

Trace form

\( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9} + O(q^{10}) \) \( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9} + 5796840 q^{10} + 193920 q^{12} - 80775396 q^{13} + 175232064 q^{14} - 353013504 q^{16} - 120131764 q^{17} + 1599402372 q^{18} - 5047343200 q^{20} + 1226658048 q^{21} + 9916985760 q^{22} - 24092176896 q^{24} + 3942973410 q^{25} + 39549467048 q^{26} - 65094731520 q^{28} - 8035796644 q^{29} + 99698873280 q^{30} - 85711465472 q^{32} - 37769804160 q^{33} + 98089165512 q^{34} - 27478990320 q^{36} + 31334118396 q^{37} - 165268841760 q^{38} + 435607171200 q^{40} + 83362750892 q^{41} - 830203906560 q^{42} + 915657452160 q^{44} + 271078769820 q^{45} - 1712365889856 q^{46} + 2292961843200 q^{48} - 551978693658 q^{49} - 1639579094580 q^{50} + 1057159118496 q^{52} + 76712275004 q^{53} + 445471858368 q^{54} - 560223046656 q^{56} - 2647253865600 q^{57} + 4483777382184 q^{58} - 9544013748480 q^{60} + 6210000787932 q^{61} + 10375644284160 q^{62} - 14398852657152 q^{64} - 7189912943720 q^{65} + 15071210499840 q^{66} - 18507298307296 q^{68} + 19348372347648 q^{69} + 12679529923200 q^{70} - 5286233111232 q^{72} - 29882649313236 q^{73} - 1536652566808 q^{74} + 21457134000000 q^{76} + 37339673521920 q^{77} - 29727224255040 q^{78} + 57843429624320 q^{80} - 98651978873946 q^{81} - 71900577251064 q^{82} + 102961968764928 q^{84} + 151199882653560 q^{85} - 100164269733216 q^{86} + 51557990330880 q^{88} - 180966014731924 q^{89} - 84934442792280 q^{90} + 82241452266240 q^{92} + 295002300748800 q^{93} - 40381697410176 q^{94} - 82703070928896 q^{96} - 345459072299124 q^{97} + 121406102961892 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(4))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4.15.b \(\chi_{4}(3, \cdot)\) 4.15.b.a 6 1