Properties

Label 1815.2.x
Level $1815$
Weight $2$
Character orbit 1815.x
Rep. character $\chi_{1815}(112,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $864$
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.x (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 864 1440
Cusp forms 1920 864 1056
Eisenstein series 384 0 384

Trace form

\( 864q + 8q^{5} + 20q^{7} + O(q^{10}) \) \( 864q + 8q^{5} + 20q^{7} + 16q^{12} + 12q^{15} + 248q^{16} + 20q^{17} + 60q^{20} - 32q^{23} + 32q^{25} + 16q^{26} + 60q^{28} + 40q^{30} - 16q^{31} + 216q^{36} - 8q^{37} - 56q^{38} + 120q^{41} - 12q^{42} + 200q^{46} - 60q^{47} - 48q^{48} - 80q^{50} - 40q^{51} - 40q^{52} - 36q^{53} + 16q^{56} - 40q^{57} - 20q^{58} - 48q^{60} - 40q^{61} - 80q^{62} - 20q^{63} + 112q^{67} - 80q^{68} + 108q^{70} - 64q^{71} + 60q^{73} + 16q^{75} + 192q^{78} + 40q^{80} + 216q^{81} - 56q^{82} + 200q^{83} + 80q^{85} + 96q^{86} - 88q^{91} - 60q^{92} + 72q^{93} - 60q^{95} - 32q^{97} + O(q^{100}) \)

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

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