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Properties

Label 64.8
Level 64
Weight 8
Dimension 493
Nonzero newspaces 4
Newform subspaces 15
Sturm bound 2048
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 15 \)
Sturm bound: \(2048\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(64))\).

Total New Old
Modular forms 932 515 417
Cusp forms 860 493 367
Eisenstein series 72 22 50

Trace form

\( 493 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 2197 q^{9} + O(q^{10}) \) \( 493 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 2197 q^{9} - 8 q^{10} - 1210 q^{11} - 8 q^{12} - 7072 q^{13} - 8 q^{14} + 26996 q^{15} - 8 q^{16} - 5830 q^{17} - 8 q^{18} - 60590 q^{19} - 8 q^{20} + 36172 q^{21} + 274448 q^{22} - 8 q^{23} - 598048 q^{24} - 13639 q^{25} + 727952 q^{26} + 233664 q^{27} + 390912 q^{28} - 103384 q^{29} - 1739928 q^{30} - 357488 q^{31} - 1071328 q^{32} - 400444 q^{33} + 403152 q^{34} + 251996 q^{35} + 4069512 q^{36} + 1465168 q^{37} + 1244912 q^{38} - 8 q^{39} - 2686368 q^{40} - 2967562 q^{41} - 3858928 q^{42} - 569762 q^{43} + 3370464 q^{44} + 1417956 q^{45} - 8 q^{46} + 2076456 q^{47} - 8 q^{48} + 1845625 q^{49} - 2317424 q^{50} - 8596172 q^{51} + 10204936 q^{52} - 3866000 q^{53} - 1259720 q^{54} + 8382008 q^{55} - 10737280 q^{56} + 4470496 q^{57} - 10358144 q^{58} + 8537006 q^{59} + 4336408 q^{60} + 307424 q^{61} + 10348520 q^{62} - 28298884 q^{63} + 22837144 q^{64} - 916536 q^{65} + 7515224 q^{66} + 9445810 q^{67} - 8750072 q^{68} - 1865444 q^{69} - 35990312 q^{70} + 24697400 q^{71} - 22727312 q^{72} - 2836490 q^{73} + 4214384 q^{74} - 28733598 q^{75} + 38942904 q^{76} + 10982156 q^{77} + 68832880 q^{78} + 9075160 q^{79} - 78362464 q^{80} - 10077611 q^{81} - 49314648 q^{82} - 4531206 q^{83} + 17056808 q^{84} + 4452048 q^{85} + 69535536 q^{86} - 8 q^{87} + 52517832 q^{88} + 20895686 q^{89} + 31733992 q^{90} - 2587660 q^{91} - 54440784 q^{92} - 15434624 q^{93} - 74691560 q^{94} + 4900620 q^{95} - 112868992 q^{96} - 33071086 q^{97} - 62769040 q^{98} - 18797518 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.8.a \(\chi_{64}(1, \cdot)\) 64.8.a.a 1 1
64.8.a.b 1
64.8.a.c 1
64.8.a.d 1
64.8.a.e 1
64.8.a.f 1
64.8.a.g 1
64.8.a.h 2
64.8.a.i 2
64.8.a.j 2
64.8.b \(\chi_{64}(33, \cdot)\) 64.8.b.a 2 1
64.8.b.b 4
64.8.b.c 8
64.8.e \(\chi_{64}(17, \cdot)\) 64.8.e.a 26 2
64.8.g \(\chi_{64}(9, \cdot)\) None 0 4
64.8.i \(\chi_{64}(5, \cdot)\) 64.8.i.a 440 8

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)