Properties

Label 1815.2.j
Level $1815$
Weight $2$
Character orbit 1815.j
Rep. character $\chi_{1815}(967,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 576 216 360
Cusp forms 480 216 264
Eisenstein series 96 0 96

Trace form

\( 216q - 8q^{5} + O(q^{10}) \) \( 216q - 8q^{5} - 16q^{12} + 8q^{15} - 248q^{16} + 40q^{20} + 32q^{23} + 8q^{25} - 16q^{26} + 16q^{31} - 216q^{36} + 8q^{37} + 56q^{38} - 8q^{42} - 32q^{48} - 24q^{53} - 176q^{56} - 32q^{60} + 48q^{67} - 8q^{70} + 64q^{71} - 16q^{75} + 48q^{78} + 160q^{80} - 216q^{81} + 96q^{82} - 96q^{86} + 48q^{91} - 40q^{92} + 48q^{93} - 88q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)