Properties

Label 1815.2.bi
Level $1815$
Weight $2$
Character orbit 1815.bi
Rep. character $\chi_{1815}(43,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $2640$
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.bi (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 5360 2640 2720
Cusp forms 5200 2640 2560
Eisenstein series 160 0 160

Trace form

\( 2640q - 8q^{5} + O(q^{10}) \) \( 2640q - 8q^{5} + 44q^{10} + 8q^{11} - 16q^{12} + 44q^{13} + 8q^{15} + 264q^{16} + 40q^{20} + 56q^{22} + 32q^{23} + 8q^{25} + 16q^{26} + 16q^{31} - 16q^{33} + 264q^{36} - 124q^{37} + 56q^{38} - 8q^{42} - 32q^{48} - 220q^{50} - 24q^{53} - 136q^{55} + 384q^{56} + 48q^{58} - 32q^{60} + 16q^{66} + 192q^{67} + 112q^{70} + 16q^{75} - 264q^{76} - 24q^{77} + 80q^{80} - 2640q^{81} + 48q^{82} + 176q^{85} - 64q^{86} - 104q^{88} - 16q^{91} + 320q^{92} + 48q^{93} - 88q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)