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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

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

Display 100 coefficients 10 coefficients

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

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