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Properties

Label 1110.4.bf
Level $1110$
Weight $4$
Character orbit 1110.bf
Rep. character $\chi_{1110}(97,\cdot)$
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.bf (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

\( 456 q - 8 q^{2} - 912 q^{4} - 20 q^{5} + 64 q^{8} + O(q^{10}) \) \( 456 q - 8 q^{2} - 912 q^{4} - 20 q^{5} + 64 q^{8} + 104 q^{10} + 80 q^{13} - 32 q^{14} - 3648 q^{16} - 360 q^{17} - 424 q^{19} + 160 q^{20} - 12 q^{25} - 608 q^{26} - 708 q^{29} + 144 q^{30} - 560 q^{31} - 128 q^{32} - 2624 q^{35} + 956 q^{37} + 624 q^{39} - 352 q^{40} - 1380 q^{41} - 224 q^{43} - 672 q^{44} + 216 q^{45} + 768 q^{49} - 1392 q^{50} + 672 q^{51} + 320 q^{52} - 2580 q^{53} + 688 q^{55} + 64 q^{56} + 1464 q^{57} - 1224 q^{58} + 104 q^{59} + 5432 q^{61} + 32 q^{62} + 29184 q^{64} + 384 q^{65} + 624 q^{66} - 992 q^{67} - 192 q^{69} - 1008 q^{70} - 1072 q^{71} + 296 q^{73} - 4880 q^{74} - 192 q^{75} - 64 q^{76} + 1312 q^{77} - 4312 q^{79} - 320 q^{80} + 18468 q^{81} + 2688 q^{83} - 1312 q^{86} + 708 q^{89} + 1640 q^{91} + 456 q^{93} - 256 q^{94} + 8064 q^{95} + 7584 q^{98} + O(q^{100}) \)

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

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