Properties

Label 1110.2.bo
Level $1110$
Weight $2$
Character orbit 1110.bo
Rep. character $\chi_{1110}(29,\cdot)$
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.bo (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

\( 304q - 8q^{9} + O(q^{10}) \) \( 304q - 8q^{9} + 4q^{15} + 152q^{16} - 16q^{19} + 96q^{31} - 8q^{34} + 16q^{39} - 24q^{40} - 32q^{45} + 16q^{46} + 168q^{49} - 40q^{51} - 40q^{55} + 8q^{60} - 96q^{61} - 48q^{66} + 64q^{69} - 8q^{70} - 112q^{75} - 16q^{76} - 24q^{79} + 24q^{81} - 20q^{90} + 64q^{91} + 48q^{94} - 120q^{99} + O(q^{100}) \)

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

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