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Properties

Label 1110.4.bi
Level $1110$
Weight $4$
Character orbit 1110.bi
Rep. character $\chi_{1110}(193,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $456$
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.bi (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
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 456 2312
Cusp forms 2704 456 2248
Eisenstein series 64 0 64

Trace form

\( 456 q + 912 q^{4} - 24 q^{5} + O(q^{10}) \) \( 456 q + 912 q^{4} - 24 q^{5} + 104 q^{10} + 32 q^{14} - 3648 q^{16} - 68 q^{17} + 72 q^{18} + 424 q^{19} - 192 q^{20} + 288 q^{22} + 144 q^{25} - 608 q^{26} + 708 q^{29} + 144 q^{30} - 560 q^{31} - 640 q^{35} - 40 q^{37} - 624 q^{39} + 64 q^{40} - 1380 q^{41} + 672 q^{44} - 180 q^{45} - 768 q^{49} + 1472 q^{50} + 672 q^{51} - 2580 q^{53} + 2896 q^{55} + 64 q^{56} - 216 q^{57} - 432 q^{58} - 104 q^{59} + 5432 q^{61} - 32 q^{62} - 29184 q^{64} - 384 q^{65} + 624 q^{66} + 2720 q^{67} - 544 q^{68} + 192 q^{69} - 1008 q^{70} - 1072 q^{71} - 288 q^{72} - 296 q^{73} + 4880 q^{74} - 192 q^{75} - 64 q^{76} - 1312 q^{77} + 4312 q^{79} - 384 q^{80} + 18468 q^{81} + 704 q^{82} - 2688 q^{83} - 1312 q^{86} + 2304 q^{88} - 708 q^{89} + 1640 q^{91} + 1368 q^{93} + 256 q^{94} + 15168 q^{95} - 2800 q^{97} + 1000 q^{98} + O(q^{100}) \)

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

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