Properties

Label 1380.2.h
Level $1380$
Weight $2$
Character orbit 1380.h
Rep. character $\chi_{1380}(1151,\cdot)$
Character field $\Q$
Dimension $176$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 296 176 120
Cusp forms 280 176 104
Eisenstein series 16 0 16

Trace form

\( 176q + 6q^{6} + 8q^{9} + O(q^{10}) \) \( 176q + 6q^{6} + 8q^{9} - 14q^{12} + 16q^{13} - 26q^{18} - 24q^{22} + 4q^{24} - 176q^{25} - 24q^{28} - 16q^{30} + 32q^{33} + 24q^{34} + 10q^{36} - 16q^{37} + 64q^{42} + 38q^{48} - 224q^{49} + 60q^{52} + 20q^{54} - 48q^{57} + 36q^{58} + 28q^{60} - 16q^{61} + 12q^{64} - 12q^{66} + 24q^{70} - 44q^{72} + 16q^{76} - 6q^{78} - 40q^{81} + 4q^{82} - 88q^{84} - 40q^{88} - 36q^{90} - 48q^{93} - 36q^{94} + 30q^{96} + 96q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)