Properties

Label 32.3
Level 32
Weight 3
Dimension 31
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 192
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(32))\).

Total New Old
Modular forms 80 41 39
Cusp forms 48 31 17
Eisenstein series 32 10 22

Trace form

\( 31q - 4q^{2} - 2q^{3} - 4q^{4} - 4q^{6} - 4q^{7} - 4q^{8} - 23q^{9} + O(q^{10}) \) \( 31q - 4q^{2} - 2q^{3} - 4q^{4} - 4q^{6} - 4q^{7} - 4q^{8} - 23q^{9} - 44q^{10} - 18q^{11} - 52q^{12} - 32q^{13} - 20q^{14} - 8q^{15} + 16q^{16} + 38q^{17} + 56q^{18} + 30q^{19} + 76q^{20} + 60q^{21} + 144q^{22} - 68q^{23} + 208q^{24} - 21q^{25} + 96q^{26} - 128q^{27} + 56q^{28} - 32q^{29} + 20q^{30} - 24q^{32} - 4q^{33} - 48q^{34} + 92q^{35} - 336q^{36} - 64q^{37} - 396q^{38} + 188q^{39} - 408q^{40} - 78q^{41} - 424q^{42} + 78q^{43} - 188q^{44} - 68q^{45} - 36q^{46} - 8q^{47} + 48q^{48} + 19q^{49} + 308q^{50} + 228q^{51} + 420q^{52} - 32q^{53} + 592q^{54} + 252q^{55} + 552q^{56} + 160q^{57} + 528q^{58} + 206q^{59} + 440q^{60} + 96q^{61} + 216q^{62} - 232q^{64} - 64q^{65} - 580q^{66} - 226q^{67} - 368q^{68} - 132q^{69} - 664q^{70} - 260q^{71} - 748q^{72} - 14q^{73} - 532q^{74} - 438q^{75} - 516q^{76} + 156q^{77} - 236q^{78} - 520q^{79} + 312q^{80} - 201q^{81} + 636q^{82} - 642q^{83} + 992q^{84} + 168q^{85} + 688q^{86} - 452q^{87} + 672q^{88} + 82q^{89} + 872q^{90} - 196q^{91} + 616q^{92} + 288q^{93} + 40q^{94} - 128q^{96} - 130q^{97} - 328q^{98} + 286q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.3.c \(\chi_{32}(31, \cdot)\) 32.3.c.a 2 1
32.3.d \(\chi_{32}(15, \cdot)\) 32.3.d.a 1 1
32.3.f \(\chi_{32}(7, \cdot)\) None 0 2
32.3.h \(\chi_{32}(3, \cdot)\) 32.3.h.a 28 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

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