Properties

Label 64.3
Level 64
Weight 3
Dimension 133
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 768
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(768\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(64))\).

Total New Old
Modular forms 292 155 137
Cusp forms 220 133 87
Eisenstein series 72 22 50

Trace form

\( 133 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} - q^{9} + O(q^{10}) \) \( 133 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} - q^{9} - 8 q^{10} + 10 q^{11} - 8 q^{12} + 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 30 q^{17} - 8 q^{18} - 38 q^{19} - 8 q^{20} - 92 q^{21} - 80 q^{22} - 68 q^{23} - 288 q^{24} - 131 q^{25} - 208 q^{26} - 72 q^{27} - 128 q^{28} - 40 q^{29} - 88 q^{30} - 16 q^{31} + 32 q^{32} + 76 q^{33} + 112 q^{34} + 92 q^{35} + 392 q^{36} + 168 q^{37} + 272 q^{38} + 188 q^{39} + 352 q^{40} + 246 q^{41} + 432 q^{42} + 106 q^{43} + 96 q^{44} + 140 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 95 q^{49} + 304 q^{50} - 548 q^{51} + 520 q^{52} - 152 q^{53} + 568 q^{54} - 772 q^{55} + 384 q^{56} - 248 q^{57} + 352 q^{58} - 470 q^{59} + 280 q^{60} - 120 q^{61} + 8 q^{62} - 104 q^{64} + 72 q^{65} - 264 q^{66} + 538 q^{67} - 248 q^{68} + 196 q^{69} - 680 q^{70} + 764 q^{71} - 656 q^{72} + 246 q^{73} - 624 q^{74} + 998 q^{75} - 840 q^{76} - 156 q^{77} - 1136 q^{78} + 504 q^{79} - 1376 q^{80} - 427 q^{81} - 1048 q^{82} - 326 q^{83} - 1240 q^{84} - 472 q^{85} - 944 q^{86} - 452 q^{87} - 568 q^{88} - 554 q^{89} - 728 q^{90} - 196 q^{91} - 464 q^{92} - 368 q^{93} - 104 q^{94} - 16 q^{95} + 128 q^{96} + 202 q^{97} + 400 q^{98} + 290 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
64.3.c \(\chi_{64}(63, \cdot)\) 64.3.c.a 1 1
64.3.c.b 2
64.3.d \(\chi_{64}(31, \cdot)\) 64.3.d.a 4 1
64.3.f \(\chi_{64}(15, \cdot)\) 64.3.f.a 6 2
64.3.h \(\chi_{64}(7, \cdot)\) None 0 4
64.3.j \(\chi_{64}(3, \cdot)\) 64.3.j.a 120 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

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