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Properties

Label 1110.4.d
Level $1110$
Weight $4$
Character orbit 1110.d
Rep. character $\chi_{1110}(889,\cdot)$
Character field $\Q$
Dimension $108$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
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 692 108 584
Cusp forms 676 108 568
Eisenstein series 16 0 16

Trace form

\( 108 q - 432 q^{4} - 32 q^{5} + 24 q^{6} - 972 q^{9} + O(q^{10}) \) \( 108 q - 432 q^{4} - 32 q^{5} + 24 q^{6} - 972 q^{9} + 24 q^{10} - 224 q^{11} + 132 q^{15} + 1728 q^{16} - 56 q^{19} + 128 q^{20} - 96 q^{24} + 596 q^{25} - 128 q^{29} - 552 q^{31} + 232 q^{35} + 3888 q^{36} - 96 q^{40} + 896 q^{44} + 288 q^{45} - 5268 q^{49} + 408 q^{51} - 216 q^{54} - 1120 q^{55} + 928 q^{59} - 528 q^{60} - 1992 q^{61} - 6912 q^{64} - 3864 q^{65} + 1056 q^{66} + 1392 q^{69} + 144 q^{70} + 1120 q^{71} + 432 q^{75} + 224 q^{76} + 3080 q^{79} - 512 q^{80} + 8748 q^{81} - 2040 q^{85} - 672 q^{86} - 768 q^{89} - 216 q^{90} + 1712 q^{91} - 2816 q^{94} + 2192 q^{95} + 384 q^{96} + 2016 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)