Properties

Label 1380.2.z
Level $1380$
Weight $2$
Character orbit 1380.z
Rep. character $\chi_{1380}(451,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $960$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.z (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

Total New Old
Modular forms 2960 960 2000
Cusp forms 2800 960 1840
Eisenstein series 160 0 160

Trace form

\( 960q + 8q^{2} + 4q^{4} + 4q^{6} + 8q^{8} + 96q^{9} + O(q^{10}) \) \( 960q + 8q^{2} + 4q^{4} + 4q^{6} + 8q^{8} + 96q^{9} + 12q^{16} - 8q^{18} - 4q^{24} + 96q^{25} + 40q^{26} - 64q^{29} - 32q^{32} + 22q^{34} + 40q^{36} + 220q^{38} + 22q^{40} + 16q^{41} + 44q^{44} + 136q^{46} + 144q^{48} - 80q^{49} + 36q^{50} + 32q^{52} + 18q^{54} + 220q^{56} + 60q^{58} + 22q^{60} - 48q^{62} + 52q^{64} + 16q^{69} - 8q^{72} - 44q^{74} + 288q^{77} - 96q^{81} - 224q^{82} - 32q^{85} - 352q^{88} + 176q^{89} - 364q^{92} - 332q^{94} + 4q^{96} + 176q^{97} - 400q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)