Properties

Label 1110.2.m
Level $1110$
Weight $2$
Character orbit 1110.m
Rep. character $\chi_{1110}(593,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Sturm bound $456$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1110, [\chi])\).

Total New Old
Modular forms 472 144 328
Cusp forms 440 144 296
Eisenstein series 32 0 32

Trace form

\( 144q + 8q^{6} + 8q^{7} + O(q^{10}) \) \( 144q + 8q^{6} + 8q^{7} - 8q^{10} - 16q^{13} - 24q^{15} - 144q^{16} - 16q^{18} - 16q^{21} - 8q^{22} + 24q^{27} + 8q^{28} + 16q^{33} + 8q^{36} - 48q^{43} - 16q^{45} - 48q^{46} + 48q^{51} + 16q^{52} - 8q^{55} + 56q^{58} + 16q^{60} + 48q^{61} + 8q^{63} - 48q^{66} + 16q^{67} - 24q^{70} + 16q^{72} + 56q^{73} + 40q^{75} + 20q^{78} + 24q^{81} - 32q^{82} + 48q^{85} - 64q^{87} - 8q^{88} + 96q^{91} - 80q^{93} - 8q^{96} - 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)