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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

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

Display 100 coefficients 10 coefficients

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 available 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

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