Properties

Label 1815.2.w
Level $1815$
Weight $2$
Character orbit 1815.w
Rep. character $\chi_{1815}(323,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1600$
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.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2304 1856 448
Cusp forms 1920 1600 320
Eisenstein series 384 256 128

Trace form

\( 1600q + 10q^{3} + 12q^{6} + 20q^{7} + O(q^{10}) \) \( 1600q + 10q^{3} + 12q^{6} + 20q^{7} + 40q^{10} + 20q^{12} + 4q^{13} + 22q^{15} + 328q^{16} - 2q^{18} + 24q^{21} + 60q^{25} + 22q^{27} - 8q^{28} + 26q^{30} + 8q^{31} + 124q^{36} - 28q^{37} - 52q^{40} - 14q^{42} - 52q^{45} - 14q^{48} + 116q^{51} - 12q^{52} - 30q^{57} - 136q^{58} - 98q^{60} + 14q^{63} - 400q^{67} - 56q^{70} - 92q^{72} + 80q^{73} + 38q^{75} + 176q^{76} - 100q^{78} - 72q^{81} - 28q^{82} + 12q^{85} + 36q^{87} - 16q^{90} - 128q^{91} + 26q^{93} - 152q^{96} + 108q^{97} + O(q^{100}) \)

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

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