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Properties

Label 64.12
Level 64
Weight 12
Dimension 781
Nonzero newspaces 4
Newform subspaces 18
Sturm bound 3072
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 18 \)
Sturm bound: \(3072\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(64))\).

Total New Old
Modular forms 1444 803 641
Cusp forms 1372 781 591
Eisenstein series 72 22 50

Trace form

\( 781 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 177157 q^{9} + O(q^{10}) \) \( 781 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 177157 q^{9} - 8 q^{10} + 540838 q^{11} - 8 q^{12} - 3087744 q^{13} - 8 q^{14} + 6074996 q^{15} - 8 q^{16} - 10558950 q^{17} - 8 q^{18} + 11291282 q^{19} - 8 q^{20} + 838828 q^{21} - 511984 q^{22} - 8 q^{23} + 356568032 q^{24} - 185556919 q^{25} - 435240048 q^{26} + 66463296 q^{27} + 717718272 q^{28} + 155346408 q^{29} - 1045605528 q^{30} - 343549808 q^{31} - 757771488 q^{32} + 440337764 q^{33} + 1807630032 q^{34} + 434731676 q^{35} - 80564088 q^{36} - 1408304464 q^{37} - 3605242128 q^{38} - 8 q^{39} + 4395265632 q^{40} + 3967114230 q^{41} - 1501551088 q^{42} - 3824193666 q^{43} + 5315103200 q^{44} - 140819964 q^{45} - 8 q^{46} + 4586900136 q^{47} - 8 q^{48} + 1949805273 q^{49} + 18403862416 q^{50} - 6625360652 q^{51} - 28023036152 q^{52} - 443534000 q^{53} + 21121591096 q^{54} - 38245610952 q^{55} + 20872814976 q^{56} + 874003456 q^{57} - 42974179712 q^{58} + 45029736142 q^{59} - 41245373672 q^{60} + 14349096960 q^{61} + 33730681832 q^{62} - 107152961284 q^{63} + 79789873048 q^{64} + 6269030024 q^{65} - 55611066280 q^{66} + 104600299250 q^{67} - 71020106744 q^{68} + 32004704956 q^{69} + 6265111768 q^{70} - 87355804104 q^{71} + 162846276976 q^{72} - 58470736906 q^{73} + 35840938608 q^{74} + 83935728642 q^{75} - 240042346312 q^{76} + 28136789996 q^{77} + 72574459504 q^{78} - 267117757352 q^{79} + 105524494496 q^{80} + 234475534357 q^{81} + 347273667752 q^{82} - 55713221126 q^{83} - 409345172440 q^{84} - 267563134672 q^{85} - 424301502672 q^{86} - 8 q^{87} + 220768887752 q^{88} + 448809825670 q^{89} + 862428149992 q^{90} + 147369662708 q^{91} + 158126049456 q^{92} - 232234324544 q^{93} - 594887103464 q^{94} - 375702304500 q^{95} - 939816536704 q^{96} - 218906239822 q^{97} + 127131707504 q^{98} + 286272748274 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(64))\)

We only show spaces with even 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
64.12.a \(\chi_{64}(1, \cdot)\) 64.12.a.a 1 1
64.12.a.b 1
64.12.a.c 1
64.12.a.d 1
64.12.a.e 1
64.12.a.f 1
64.12.a.g 1
64.12.a.h 2
64.12.a.i 2
64.12.a.j 2
64.12.a.k 2
64.12.a.l 3
64.12.a.m 3
64.12.b \(\chi_{64}(33, \cdot)\) 64.12.b.a 2 1
64.12.b.b 4
64.12.b.c 16
64.12.e \(\chi_{64}(17, \cdot)\) 64.12.e.a 42 2
64.12.g \(\chi_{64}(9, \cdot)\) None 0 4
64.12.i \(\chi_{64}(5, \cdot)\) 64.12.i.a 696 8

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)