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Properties

Label 1110.4.bg
Level $1110$
Weight $4$
Character orbit 1110.bg
Rep. character $\chi_{1110}(233,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $912$
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.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(912\)

Dimensions

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

Total New Old
Modular forms 2768 912 1856
Cusp forms 2704 912 1792
Eisenstein series 64 0 64

Trace form

\( 912 q - 8 q^{3} + O(q^{10}) \) \( 912 q - 8 q^{3} - 32 q^{12} + 12 q^{15} + 7296 q^{16} - 1080 q^{25} + 40 q^{27} - 336 q^{30} - 352 q^{33} - 456 q^{37} - 192 q^{40} - 2616 q^{42} - 288 q^{46} - 256 q^{48} - 2592 q^{55} + 336 q^{57} + 1104 q^{58} + 576 q^{61} - 2736 q^{67} - 1008 q^{70} + 5856 q^{73} - 10928 q^{75} - 1240 q^{78} - 4368 q^{81} + 3024 q^{85} + 1332 q^{87} - 1560 q^{90} + 5904 q^{91} - 4452 q^{93} + O(q^{100}) \)

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

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