Properties

Label 1815.2.f
Level $1815$
Weight $2$
Character orbit 1815.f
Rep. character $\chi_{1815}(1451,\cdot)$
Character field $\Q$
Dimension $144$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 288 144 144
Cusp forms 240 144 96
Eisenstein series 48 0 48

Trace form

\( 144q + 4q^{3} + 144q^{4} - 8q^{9} + O(q^{10}) \) \( 144q + 4q^{3} + 144q^{4} - 8q^{9} + 12q^{12} + 4q^{15} + 176q^{16} - 144q^{25} - 20q^{27} + 24q^{34} + 44q^{36} - 24q^{37} - 12q^{42} + 32q^{48} - 152q^{49} - 12q^{60} + 160q^{64} - 88q^{67} + 40q^{69} - 24q^{70} - 4q^{75} - 92q^{78} + 64q^{82} + 56q^{91} + 72q^{93} - 32q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)