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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

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

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

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