Properties

Label 64.5
Level 64
Weight 5
Dimension 277
Nonzero newspaces 4
Newform subspaces 8
Sturm bound 1280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
Sturm bound: \(1280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(64))\).

Total New Old
Modular forms 548 299 249
Cusp forms 476 277 199
Eisenstein series 72 22 50

Trace form

\( 277 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 71 q^{9} + O(q^{10}) \) \( 277 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 71 q^{9} - 8 q^{10} - 102 q^{11} - 8 q^{12} - 360 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} + 466 q^{17} - 8 q^{18} + 698 q^{19} - 8 q^{20} - 44 q^{21} - 2672 q^{22} - 1156 q^{23} - 288 q^{24} + 709 q^{25} + 5392 q^{26} + 1656 q^{27} + 5632 q^{28} + 1720 q^{29} + 4712 q^{30} - 16 q^{31} - 2528 q^{32} - 3812 q^{33} - 7088 q^{34} - 1348 q^{35} - 18808 q^{36} - 1576 q^{37} - 7568 q^{38} - 2692 q^{39} + 352 q^{40} - 1546 q^{41} + 16272 q^{42} - 1702 q^{43} + 8416 q^{44} - 1636 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} + 593 q^{49} + 21520 q^{50} - 13124 q^{51} + 8968 q^{52} + 10072 q^{53} - 15560 q^{54} + 35324 q^{55} - 24704 q^{56} + 9880 q^{57} - 32768 q^{58} + 28890 q^{59} - 31976 q^{60} - 8296 q^{61} - 6040 q^{62} + 12184 q^{64} + 2088 q^{65} + 35544 q^{66} - 45766 q^{67} + 26632 q^{68} - 9452 q^{69} + 61144 q^{70} - 59908 q^{71} + 40816 q^{72} - 17930 q^{73} + 16624 q^{74} - 22186 q^{75} - 14152 q^{76} - 16812 q^{77} - 103952 q^{78} + 50168 q^{79} - 115040 q^{80} + 1589 q^{81} - 5208 q^{82} + 17274 q^{83} + 57896 q^{84} + 41688 q^{85} + 85168 q^{86} + 49276 q^{87} + 71112 q^{88} + 66998 q^{89} + 111592 q^{90} + 28028 q^{91} + 79792 q^{92} + 33328 q^{93} + 17944 q^{94} - 16 q^{95} - 25984 q^{96} - 42598 q^{97} - 76304 q^{98} - 48574 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.5.c \(\chi_{64}(63, \cdot)\) 64.5.c.a 1 1
64.5.c.b 2
64.5.c.c 2
64.5.c.d 2
64.5.d \(\chi_{64}(31, \cdot)\) 64.5.d.a 4 1
64.5.d.b 4
64.5.f \(\chi_{64}(15, \cdot)\) 64.5.f.a 14 2
64.5.h \(\chi_{64}(7, \cdot)\) None 0 4
64.5.j \(\chi_{64}(3, \cdot)\) 64.5.j.a 248 8

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

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