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Properties

Label 1110.4.ba
Level $1110$
Weight $4$
Character orbit 1110.ba
Rep. character $\chi_{1110}(529,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $232$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(912\)

Dimensions

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

Total New Old
Modular forms 1384 232 1152
Cusp forms 1352 232 1120
Eisenstein series 32 0 32

Trace form

\( 232 q - 464 q^{4} + 30 q^{5} + 1044 q^{9} + O(q^{10}) \) \( 232 q - 464 q^{4} + 30 q^{5} + 1044 q^{9} + 40 q^{10} - 56 q^{11} - 1856 q^{16} + 204 q^{19} - 120 q^{20} + 72 q^{21} - 86 q^{25} + 16 q^{26} - 24 q^{30} + 624 q^{34} + 1968 q^{35} - 8352 q^{36} + 1044 q^{39} - 80 q^{40} - 308 q^{41} + 112 q^{44} - 56 q^{46} + 7068 q^{49} + 1140 q^{50} - 2016 q^{55} - 2772 q^{59} - 4164 q^{61} + 14848 q^{64} + 2812 q^{65} + 288 q^{69} - 1688 q^{70} + 2328 q^{71} - 3640 q^{74} + 96 q^{75} - 816 q^{76} + 480 q^{79} - 9396 q^{81} - 576 q^{84} + 3540 q^{85} + 480 q^{86} + 5544 q^{89} + 180 q^{90} - 10968 q^{91} + 1008 q^{94} + 1680 q^{95} - 252 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)