Properties

Label 1110.2.n
Level $1110$
Weight $2$
Character orbit 1110.n
Rep. character $\chi_{1110}(443,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $152$
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.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
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 472 152 320
Cusp forms 440 152 288
Eisenstein series 32 0 32

Trace form

\( 152q + 8q^{3} + O(q^{10}) \) \( 152q + 8q^{3} + 8q^{12} - 152q^{16} - 64q^{25} - 16q^{27} - 24q^{30} - 8q^{33} + 24q^{37} + 16q^{40} + 16q^{46} - 8q^{48} + 16q^{58} - 16q^{67} - 16q^{70} + 16q^{73} + 80q^{75} - 20q^{78} + 144q^{81} - 96q^{85} - 96q^{90} + O(q^{100}) \)

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

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