Properties

Label 1110.2.cd
Level $1110$
Weight $2$
Character orbit 1110.cd
Rep. character $\chi_{1110}(53,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $912$
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.cd (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(456\)

Dimensions

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

Total New Old
Modular forms 2832 912 1920
Cusp forms 2640 912 1728
Eisenstein series 192 0 192

Trace form

\( 912q + 12q^{3} + O(q^{10}) \) \( 912q + 12q^{3} - 12q^{12} + 12q^{15} + 48q^{25} - 12q^{27} - 48q^{31} - 12q^{33} - 24q^{37} + 48q^{40} - 12q^{42} + 96q^{45} + 48q^{55} + 48q^{57} - 24q^{58} + 48q^{61} + 24q^{67} + 24q^{70} - 48q^{73} - 192q^{75} - 24q^{81} - 24q^{85} + 216q^{87} - 24q^{88} + 72q^{90} - 96q^{91} - 48q^{97} + O(q^{100}) \)

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

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