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Properties

Label 64.7
Level 64
Weight 7
Dimension 421
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 1792
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1792\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(64))\).

Total New Old
Modular forms 804 443 361
Cusp forms 732 421 311
Eisenstein series 72 22 50

Trace form

\( 421 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 719 q^{9} + O(q^{10}) \) \( 421 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 719 q^{9} - 8 q^{10} - 1366 q^{11} - 8 q^{12} + 5032 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 9790 q^{17} - 8 q^{18} - 3942 q^{19} - 8 q^{20} + 16516 q^{21} - 63728 q^{22} + 13116 q^{23} + 160992 q^{24} + 25549 q^{25} - 10608 q^{26} - 35784 q^{27} - 171008 q^{28} - 66408 q^{29} - 206488 q^{30} - 16 q^{31} + 117792 q^{32} + 177772 q^{33} + 278992 q^{34} + 112412 q^{35} + 365192 q^{36} - 48248 q^{37} - 200208 q^{38} - 254404 q^{39} - 575648 q^{40} - 175370 q^{41} - 173808 q^{42} + 267978 q^{43} + 480992 q^{44} + 320300 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 323583 q^{49} + 705424 q^{50} + 19612 q^{51} - 1275128 q^{52} - 301112 q^{53} - 1259720 q^{54} + 698108 q^{55} + 326528 q^{56} + 217768 q^{57} + 1770112 q^{58} - 1811446 q^{59} + 2511640 q^{60} - 196568 q^{61} + 541160 q^{62} - 1155176 q^{64} + 356232 q^{65} - 3102120 q^{66} + 3141978 q^{67} - 1847288 q^{68} - 799004 q^{69} - 2272040 q^{70} + 801020 q^{71} + 787312 q^{72} + 135926 q^{73} + 2924144 q^{74} - 4017082 q^{75} + 4565176 q^{76} + 324804 q^{77} - 3782288 q^{78} + 1721848 q^{79} - 2090336 q^{80} + 1776533 q^{81} + 6966952 q^{82} + 288314 q^{83} + 5971496 q^{84} - 801272 q^{85} - 828368 q^{86} - 2029892 q^{87} - 4695608 q^{88} - 4407402 q^{89} - 11466008 q^{90} - 302404 q^{91} - 10105424 q^{92} + 2013904 q^{93} - 2508776 q^{94} - 16 q^{95} + 3708032 q^{96} + 231018 q^{97} + 10348912 q^{98} + 277346 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(64))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
64.7.c \(\chi_{64}(63, \cdot)\) 64.7.c.a 1 1
64.7.c.b 2
64.7.c.c 2
64.7.c.d 2
64.7.c.e 4
64.7.d \(\chi_{64}(31, \cdot)\) 64.7.d.a 4 1
64.7.d.b 8
64.7.f \(\chi_{64}(15, \cdot)\) 64.7.f.a 22 2
64.7.h \(\chi_{64}(7, \cdot)\) None 0 4
64.7.j \(\chi_{64}(3, \cdot)\) 64.7.j.a 376 8

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

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