Properties

Label 1815.2.d
Level $1815$
Weight $2$
Character orbit 1815.d
Rep. character $\chi_{1815}(1814,\cdot)$
Character field $\Q$
Dimension $200$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1815, [\chi])\).

Total New Old
Modular forms 288 232 56
Cusp forms 240 200 40
Eisenstein series 48 32 16

Trace form

\( 200q - 176q^{4} + 12q^{9} + O(q^{10}) \) \( 200q - 176q^{4} + 12q^{9} - 2q^{15} + 160q^{16} - 8q^{25} + 32q^{31} - 56q^{34} - 36q^{36} - 38q^{45} + 112q^{49} + 28q^{60} - 168q^{64} + 60q^{69} + 44q^{70} - 6q^{75} + 44q^{81} + 144q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)