Properties

Label 1815.2.k
Level $1815$
Weight $2$
Character orbit 1815.k
Rep. character $\chi_{1815}(122,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $400$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 576 472 104
Cusp forms 480 400 80
Eisenstein series 96 72 24

Trace form

\( 400q + 8q^{6} + O(q^{10}) \) \( 400q + 8q^{6} - 20q^{12} + 16q^{13} - 12q^{15} - 288q^{16} + 12q^{18} + 16q^{21} - 12q^{27} - 32q^{28} - 16q^{30} + 32q^{31} - 24q^{36} + 48q^{37} - 8q^{40} + 4q^{42} - 28q^{45} - 16q^{48} - 16q^{51} - 88q^{52} - 40q^{57} + 16q^{58} + 168q^{60} - 4q^{63} - 40q^{67} + 56q^{70} - 48q^{72} + 52q^{75} - 96q^{76} + 20q^{78} + 72q^{81} + 8q^{82} + 8q^{85} - 16q^{87} + 16q^{90} + 48q^{91} - 76q^{93} - 128q^{96} - 88q^{97} + O(q^{100}) \)

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

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