Properties

Label 1110.2.bg
Level $1110$
Weight $2$
Character orbit 1110.bg
Rep. character $\chi_{1110}(233,\cdot)$
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.bg (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

\( 304 q + 4 q^{3} + O(q^{10}) \) \( 304 q + 4 q^{3} + 4 q^{12} + 12 q^{15} + 152 q^{16} + 40 q^{25} + 40 q^{27} + 24 q^{30} - 4 q^{33} - 48 q^{37} + 8 q^{40} + 12 q^{42} - 16 q^{46} + 8 q^{48} + 48 q^{55} + 48 q^{57} + 8 q^{58} - 48 q^{61} - 8 q^{67} - 8 q^{70} + 32 q^{73} + 112 q^{75} + 20 q^{78} + 24 q^{81} + 144 q^{85} + 36 q^{87} + 60 q^{90} - 192 q^{91} - 24 q^{93} + O(q^{100}) \)

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

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