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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

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

Display 100 coefficients 10 coefficients

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

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