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Properties

Label 32.2
Level 32
Weight 2
Dimension 13
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 128
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(32))\).

Total New Old
Modular forms 48 23 25
Cusp forms 17 13 4
Eisenstein series 31 10 21

Trace form

\( 13 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 6 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 7 q^{9} + O(q^{10}) \) \( 13 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 6 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 7 q^{9} + 4 q^{10} - 4 q^{11} + 12 q^{12} + 2 q^{13} + 12 q^{14} + 16 q^{16} + 2 q^{17} + 16 q^{18} - 4 q^{19} + 12 q^{20} - 4 q^{21} + 8 q^{22} + 4 q^{23} - 16 q^{24} - 5 q^{25} - 24 q^{26} + 20 q^{27} - 24 q^{28} - 14 q^{29} - 36 q^{30} + 16 q^{31} - 24 q^{32} - 8 q^{33} - 16 q^{34} + 20 q^{35} - 32 q^{36} - 6 q^{37} + 4 q^{38} + 20 q^{39} + 8 q^{40} + 6 q^{41} + 16 q^{42} + 4 q^{43} + 36 q^{44} + 14 q^{45} + 28 q^{46} + 48 q^{48} - 7 q^{49} + 36 q^{50} - 8 q^{51} + 4 q^{52} + 26 q^{53} + 8 q^{54} - 36 q^{55} + 8 q^{56} - 4 q^{57} - 8 q^{58} - 36 q^{59} - 8 q^{60} + 18 q^{61} - 24 q^{62} - 48 q^{63} - 40 q^{64} - 20 q^{65} - 28 q^{66} - 44 q^{67} + 16 q^{68} + 28 q^{69} - 16 q^{70} - 36 q^{71} + 20 q^{72} - 10 q^{73} + 12 q^{74} - 16 q^{75} - 4 q^{76} + 12 q^{77} + 36 q^{78} - 8 q^{80} + 9 q^{81} - 4 q^{82} + 36 q^{83} + 16 q^{84} + 12 q^{85} - 24 q^{86} + 52 q^{87} + 6 q^{89} + 8 q^{90} + 44 q^{91} - 40 q^{92} - 16 q^{93} + 8 q^{94} + 56 q^{95} + 10 q^{97} - 24 q^{98} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)

We only show spaces with even 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
32.2.a \(\chi_{32}(1, \cdot)\) 32.2.a.a 1 1
32.2.b \(\chi_{32}(17, \cdot)\) None 0 1
32.2.e \(\chi_{32}(9, \cdot)\) None 0 2
32.2.g \(\chi_{32}(5, \cdot)\) 32.2.g.a 4 4
32.2.g.b 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

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