Properties

Label 1110.2.bh
Level $1110$
Weight $2$
Character orbit 1110.bh
Rep. character $\chi_{1110}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $304$
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.bh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(456\)

Dimensions

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

Total New Old
Modular forms 944 304 640
Cusp forms 880 304 576
Eisenstein series 64 0 64

Trace form

\( 304q - 4q^{3} + O(q^{10}) \) \( 304q - 4q^{3} + 4q^{12} + 16q^{13} - 4q^{15} + 152q^{16} + 16q^{22} + 56q^{25} - 40q^{27} + 24q^{30} + 64q^{31} + 4q^{33} + 8q^{40} + 4q^{42} - 64q^{45} + 16q^{46} - 8q^{48} - 32q^{51} - 16q^{52} - 64q^{55} - 16q^{57} + 8q^{58} - 8q^{60} - 48q^{61} + 32q^{66} - 8q^{67} - 8q^{70} + 32q^{73} + 96q^{75} - 32q^{76} - 20q^{78} + 88q^{81} + 64q^{82} - 112q^{85} - 12q^{87} - 32q^{88} + 20q^{90} + 64q^{93} - 80q^{97} + O(q^{100}) \)

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

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