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Properties

Label 32.9
Level 32
Weight 9
Dimension 139
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 576
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(576\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(32))\).

Total New Old
Modular forms 272 149 123
Cusp forms 240 139 101
Eisenstein series 32 10 22

Trace form

\( 139 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 332 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 2759 q^{9} + O(q^{10}) \) \( 139 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 332 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 2759 q^{9} + 34996 q^{10} - 19778 q^{11} - 45364 q^{12} + 79948 q^{13} + 145580 q^{14} - 8 q^{15} - 278384 q^{16} - 182114 q^{17} - 131224 q^{18} + 167550 q^{19} + 689996 q^{20} - 98052 q^{21} + 6048 q^{22} + 845564 q^{23} - 310832 q^{24} + 673851 q^{25} + 1682096 q^{26} - 63488 q^{27} - 1807624 q^{28} - 1196212 q^{29} - 3968188 q^{30} + 2420456 q^{32} + 1564436 q^{33} + 4139280 q^{34} - 4404868 q^{35} - 2364816 q^{36} + 1262156 q^{37} - 4553644 q^{38} + 7650044 q^{39} - 14971800 q^{40} - 4292646 q^{41} + 17019656 q^{42} + 2595390 q^{43} + 13377860 q^{44} + 6951880 q^{45} + 11790684 q^{46} - 8 q^{47} - 21819984 q^{48} - 15927473 q^{49} - 49149676 q^{50} - 28917372 q^{51} - 33503196 q^{52} - 12186676 q^{53} + 82403296 q^{54} + 46326780 q^{55} + 87708200 q^{56} + 34860184 q^{57} - 37235424 q^{58} - 46004162 q^{59} - 167711176 q^{60} + 47775564 q^{61} + 23721528 q^{62} + 27135128 q^{64} + 16926232 q^{65} + 226680332 q^{66} + 59474558 q^{67} - 491760 q^{68} - 87107076 q^{69} - 167238952 q^{70} - 79832068 q^{71} - 184202092 q^{72} + 1939162 q^{73} + 28015148 q^{74} + 85394490 q^{75} + 201789948 q^{76} + 43691132 q^{77} + 473461108 q^{78} + 144406520 q^{79} - 447998920 q^{80} - 157734165 q^{81} - 231632004 q^{82} - 315240962 q^{83} + 263072 q^{84} - 34200288 q^{85} + 268005440 q^{86} - 149712644 q^{87} + 220344096 q^{88} + 132054618 q^{89} + 51924392 q^{90} + 624372476 q^{91} - 622977496 q^{92} + 118704768 q^{93} - 100742552 q^{94} + 101686144 q^{96} - 291759082 q^{97} + 721239576 q^{98} - 1075195778 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.9.c \(\chi_{32}(31, \cdot)\) 32.9.c.a 4 1
32.9.c.b 4
32.9.d \(\chi_{32}(15, \cdot)\) 32.9.d.a 1 1
32.9.d.b 6
32.9.f \(\chi_{32}(7, \cdot)\) None 0 2
32.9.h \(\chi_{32}(3, \cdot)\) 32.9.h.a 124 4

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

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