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Properties

Label 1932.2.bo
Level $1932$
Weight $2$
Character orbit 1932.bo
Rep. character $\chi_{1932}(43,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1440$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1932.bo (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1932, [\chi])\).

Total New Old
Modular forms 3920 1440 2480
Cusp forms 3760 1440 2320
Eisenstein series 160 0 160

Trace form

\( 1440 q + 4 q^{2} - 4 q^{4} + 8 q^{6} + 4 q^{8} + 144 q^{9} + O(q^{10}) \) \( 1440 q + 4 q^{2} - 4 q^{4} + 8 q^{6} + 4 q^{8} + 144 q^{9} + 12 q^{16} - 4 q^{18} - 8 q^{24} + 144 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} + 44 q^{34} + 26 q^{36} + 44 q^{40} + 154 q^{44} + 164 q^{46} + 144 q^{48} - 144 q^{49} + 86 q^{50} + 32 q^{52} + 36 q^{54} + 46 q^{58} + 44 q^{60} - 8 q^{62} + 68 q^{64} + 32 q^{69} - 4 q^{72} - 22 q^{74} - 220 q^{76} + 144 q^{77} - 144 q^{81} - 296 q^{82} - 48 q^{85} - 440 q^{86} - 22 q^{88} + 176 q^{89} + 44 q^{92} + 16 q^{93} + 120 q^{94} + 48 q^{96} + 176 q^{97} - 18 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1932, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1932, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1932, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(644, [\chi])\)\(^{\oplus 2}\)