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Properties

Label 1110.4.e
Level $1110$
Weight $4$
Character orbit 1110.e
Rep. character $\chi_{1110}(739,\cdot)$
Character field $\Q$
Dimension $116$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q\)
Sturm bound: \(912\)

Dimensions

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

Total New Old
Modular forms 692 116 576
Cusp forms 676 116 560
Eisenstein series 16 0 16

Trace form

\( 116 q + 464 q^{4} - 1044 q^{9} + O(q^{10}) \) \( 116 q + 464 q^{4} - 1044 q^{9} - 40 q^{10} + 56 q^{11} + 1856 q^{16} - 360 q^{21} - 172 q^{25} - 448 q^{26} - 48 q^{30} - 384 q^{34} - 4176 q^{36} - 160 q^{40} - 1888 q^{41} + 224 q^{44} + 2528 q^{46} - 4956 q^{49} + 7424 q^{64} - 1480 q^{65} + 176 q^{70} + 240 q^{71} - 1424 q^{74} - 96 q^{75} + 9396 q^{81} - 1440 q^{84} + 120 q^{85} + 960 q^{86} + 360 q^{90} - 720 q^{95} - 504 q^{99} + O(q^{100}) \)

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

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