Properties

Label 1380.2.o
Level $1380$
Weight $2$
Character orbit 1380.o
Rep. character $\chi_{1380}(599,\cdot)$
Character field $\Q$
Dimension $264$
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.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
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 296 264 32
Cusp forms 280 264 16
Eisenstein series 16 0 16

Trace form

\( 264q + O(q^{10}) \) \( 264q + 8q^{10} - 16q^{16} - 44q^{24} - 8q^{25} - 34q^{30} + 24q^{36} - 8q^{40} + 248q^{49} + 44q^{54} + 36q^{60} - 32q^{61} + 72q^{64} - 48q^{66} + 72q^{70} - 72q^{76} - 140q^{84} + 16q^{85} - 82q^{90} - 136q^{94} - 24q^{96} + O(q^{100}) \)

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

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