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Properties

Label 64.9
Level 64
Weight 9
Dimension 565
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 2304
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(2304\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(64))\).

Total New Old
Modular forms 1060 587 473
Cusp forms 988 565 423
Eisenstein series 72 22 50

Trace form

\( 565 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 6551 q^{9} + O(q^{10}) \) \( 565 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 6551 q^{9} - 8 q^{10} + 19770 q^{11} - 8 q^{12} - 51400 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} + 154546 q^{17} - 8 q^{18} - 167558 q^{19} - 8 q^{20} - 269900 q^{21} - 1068272 q^{22} + 845564 q^{23} + 322272 q^{24} - 1807211 q^{25} - 3364208 q^{26} - 38664 q^{27} + 3615232 q^{28} + 2132344 q^{29} + 7934312 q^{30} - 16 q^{31} - 4840928 q^{32} - 6597572 q^{33} - 8276528 q^{34} - 426628 q^{35} + 7200392 q^{36} + 431544 q^{37} + 16322032 q^{38} + 7650044 q^{39} - 1151648 q^{40} - 3247114 q^{41} - 35148528 q^{42} - 6314822 q^{43} + 22652128 q^{44} - 12249796 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} + 6369457 q^{49} - 5145200 q^{50} + 84417916 q^{51} - 45948152 q^{52} - 7237448 q^{53} + 79361848 q^{54} - 138980356 q^{55} + 56874880 q^{56} - 17203400 q^{57} - 50876288 q^{58} + 135881658 q^{59} - 163708136 q^{60} + 16294200 q^{61} - 43933720 q^{62} + 96767896 q^{64} - 60985752 q^{65} + 227317848 q^{66} - 246235526 q^{67} + 81864712 q^{68} + 73645108 q^{69} - 92889896 q^{70} + 239496188 q^{71} - 261232784 q^{72} + 47641590 q^{73} - 170028944 q^{74} - 36845386 q^{75} + 159303864 q^{76} - 99681612 q^{77} + 68388208 q^{78} - 144406536 q^{79} + 332920480 q^{80} + 345072245 q^{81} + 69799592 q^{82} + 34471674 q^{83} - 689231320 q^{84} - 146268232 q^{85} - 554580944 q^{86} - 149712644 q^{87} + 45587912 q^{88} + 113890166 q^{89} + 873269992 q^{90} + 76429052 q^{91} + 1093020592 q^{92} + 368941168 q^{93} + 310515736 q^{94} - 16 q^{95} - 468840832 q^{96} - 392821958 q^{97} - 1202501264 q^{98} - 184785790 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.9.c \(\chi_{64}(63, \cdot)\) 64.9.c.a 1 1
64.9.c.b 2
64.9.c.c 2
64.9.c.d 2
64.9.c.e 4
64.9.c.f 4
64.9.d \(\chi_{64}(31, \cdot)\) 64.9.d.a 4 1
64.9.d.b 12
64.9.f \(\chi_{64}(15, \cdot)\) 64.9.f.a 30 2
64.9.h \(\chi_{64}(7, \cdot)\) None 0 4
64.9.j \(\chi_{64}(3, \cdot)\) 64.9.j.a 504 8

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)