Properties

Label 1815.2.bb
Level $1815$
Weight $2$
Character orbit 1815.bb
Rep. character $\chi_{1815}(131,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1760$
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.bb (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 363 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2680 1760 920
Cusp forms 2600 1760 840
Eisenstein series 80 0 80

Trace form

\( 1760q + 4q^{3} - 176q^{4} - 8q^{9} + O(q^{10}) \) \( 1760q + 4q^{3} - 176q^{4} - 8q^{9} - 54q^{12} - 18q^{15} - 144q^{16} + 8q^{22} + 88q^{24} + 176q^{25} - 20q^{27} + 44q^{31} - 4q^{33} + 40q^{34} + 4q^{36} - 8q^{37} + 28q^{42} + 72q^{48} + 140q^{49} + 66q^{51} - 44q^{52} + 154q^{54} - 8q^{55} + 154q^{57} - 104q^{58} - 12q^{60} - 512q^{64} - 2q^{66} - 88q^{67} + 40q^{69} - 24q^{70} + 44q^{73} - 4q^{75} - 396q^{76} - 84q^{78} - 44q^{79} - 32q^{81} + 136q^{82} + 132q^{85} - 412q^{88} - 88q^{90} + 132q^{91} - 26q^{93} + 40q^{97} - 56q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)