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Properties

Label 1110.4.cg
Level $1110$
Weight $4$
Character orbit 1110.cg
Rep. character $\chi_{1110}(77,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2736$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1110.cg (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1110, [\chi])\).

Total New Old
Modular forms 8304 2736 5568
Cusp forms 8112 2736 5376
Eisenstein series 192 0 192

Trace form

\( 2736 q + 24 q^{3} + O(q^{10}) \) \( 2736 q + 24 q^{3} + 96 q^{12} - 12 q^{15} + 432 q^{25} + 444 q^{27} + 1056 q^{33} + 648 q^{37} - 1152 q^{40} + 2616 q^{42} + 2592 q^{55} - 336 q^{57} - 3312 q^{58} - 576 q^{61} + 8208 q^{67} + 3024 q^{70} - 8784 q^{73} + 14208 q^{75} + 2208 q^{81} + 2664 q^{85} + 13608 q^{87} - 5184 q^{88} - 11952 q^{90} - 5904 q^{91} + 4452 q^{93} - 10368 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)