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Properties

Label 332.2
Level 332
Weight 2
Dimension 1927
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 13776
Trace bound 1

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Defining parameters

Level: \( N \) = \( 332 = 2^{2} \cdot 83 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(13776\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(332))\).

Total New Old
Modular forms 3649 2091 1558
Cusp forms 3240 1927 1313
Eisenstein series 409 164 245

Trace form

\( 1927 q - 41 q^{2} - 41 q^{4} - 82 q^{5} - 41 q^{6} - 41 q^{8} - 82 q^{9} + O(q^{10}) \) \( 1927 q - 41 q^{2} - 41 q^{4} - 82 q^{5} - 41 q^{6} - 41 q^{8} - 82 q^{9} - 41 q^{10} - 41 q^{12} - 82 q^{13} - 41 q^{14} - 41 q^{16} - 82 q^{17} - 41 q^{18} - 41 q^{20} - 82 q^{21} - 41 q^{22} - 41 q^{24} - 82 q^{25} - 41 q^{26} - 41 q^{28} - 82 q^{29} - 41 q^{30} - 41 q^{32} - 82 q^{33} - 41 q^{34} - 41 q^{36} - 82 q^{37} - 41 q^{38} - 41 q^{40} - 82 q^{41} - 41 q^{42} - 41 q^{44} - 82 q^{45} - 41 q^{46} - 41 q^{48} - 82 q^{49} - 41 q^{50} - 41 q^{52} - 82 q^{53} - 41 q^{54} - 41 q^{56} - 82 q^{57} - 41 q^{58} - 41 q^{60} - 82 q^{61} - 41 q^{62} - 41 q^{64} - 82 q^{65} - 41 q^{66} - 41 q^{67} - 41 q^{68} - 205 q^{69} - 41 q^{70} - 41 q^{71} - 41 q^{72} - 205 q^{73} - 41 q^{74} - 287 q^{75} - 41 q^{76} - 205 q^{77} - 41 q^{78} - 123 q^{79} - 41 q^{80} - 246 q^{81} - 123 q^{83} - 82 q^{84} - 205 q^{85} - 41 q^{86} - 164 q^{87} - 41 q^{88} - 205 q^{89} - 41 q^{90} - 123 q^{91} - 41 q^{92} - 369 q^{93} - 41 q^{94} - 123 q^{95} - 41 q^{96} - 123 q^{97} - 41 q^{98} - 123 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(332))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
332.2.a \(\chi_{332}(1, \cdot)\) 332.2.a.a 2 1
332.2.a.b 2
332.2.a.c 3
332.2.b \(\chi_{332}(331, \cdot)\) 332.2.b.a 40 1
332.2.e \(\chi_{332}(9, \cdot)\) 332.2.e.a 280 40
332.2.h \(\chi_{332}(15, \cdot)\) 332.2.h.a 1600 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(166))\)\(^{\oplus 2}\)