Properties

Label 1380.2.bh
Level $1380$
Weight $2$
Character orbit 1380.bh
Rep. character $\chi_{1380}(71,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1920$
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.bh (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 276 \)
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 1920 1040
Cusp forms 2800 1920 880
Eisenstein series 160 0 160

Trace form

\( 1920q + 4q^{4} + 6q^{6} + O(q^{10}) \) \( 1920q + 4q^{4} + 6q^{6} + 4q^{10} + 6q^{12} + 28q^{16} - 6q^{18} - 8q^{21} + 32q^{22} + 192q^{25} - 32q^{28} - 10q^{34} - 46q^{36} + 126q^{40} - 40q^{42} + 8q^{45} + 156q^{46} + 34q^{48} + 192q^{49} + 4q^{52} + 212q^{58} + 32q^{61} - 8q^{64} + 92q^{66} - 12q^{69} - 4q^{72} + 56q^{76} - 294q^{78} + 40q^{81} - 84q^{82} - 252q^{84} - 32q^{85} - 48q^{88} + 512q^{93} + 12q^{94} - 114q^{96} + O(q^{100}) \)

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

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