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Properties

Label 1110.4.bq
Level $1110$
Weight $4$
Character orbit 1110.bq
Rep. character $\chi_{1110}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $672$
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.bq (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(912\)

Dimensions

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

Total New Old
Modular forms 4152 672 3480
Cusp forms 4056 672 3384
Eisenstein series 96 0 96

Trace form

\( 672 q + 36 q^{5} + O(q^{10}) \) \( 672 q + 36 q^{5} + 24 q^{14} - 204 q^{19} - 144 q^{20} - 288 q^{21} + 132 q^{25} + 1104 q^{26} - 144 q^{30} - 1704 q^{31} + 552 q^{34} + 3192 q^{35} + 24192 q^{36} - 1080 q^{39} + 768 q^{40} - 1968 q^{41} + 336 q^{44} + 3768 q^{46} - 1344 q^{49} - 3696 q^{50} - 1512 q^{55} + 2808 q^{59} - 3072 q^{61} + 21504 q^{64} + 492 q^{65} - 288 q^{69} + 1512 q^{70} - 2880 q^{71} - 2256 q^{74} + 816 q^{76} - 552 q^{79} - 2016 q^{84} + 1068 q^{85} - 912 q^{86} + 10356 q^{89} - 864 q^{90} + 13884 q^{91} + 4824 q^{94} - 960 q^{95} + 756 q^{99} + O(q^{100}) \)

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

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