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Properties

Label 1110.4.bc
Level $1110$
Weight $4$
Character orbit 1110.bc
Rep. character $\chi_{1110}(181,\cdot)$
Character field $\Q(\zeta_{9})$
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.bc (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(912\)

Dimensions

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

Total New Old
Modular forms 4152 456 3696
Cusp forms 4056 456 3600
Eisenstein series 96 0 96

Trace form

\( 456 q - 156 q^{7} + O(q^{10}) \) \( 456 q - 156 q^{7} + 120 q^{10} - 264 q^{13} + 24 q^{14} - 684 q^{19} + 468 q^{21} + 324 q^{27} + 96 q^{28} + 480 q^{29} + 1704 q^{31} - 1152 q^{33} - 1224 q^{34} + 240 q^{35} + 16416 q^{36} - 2604 q^{37} - 1632 q^{38} - 2340 q^{39} - 288 q^{42} + 576 q^{43} + 336 q^{44} - 1176 q^{46} + 1776 q^{47} + 576 q^{48} + 1956 q^{49} - 48 q^{52} - 540 q^{55} + 648 q^{59} - 1152 q^{61} - 2208 q^{62} - 14592 q^{64} - 420 q^{65} + 948 q^{67} + 3072 q^{68} - 2088 q^{69} + 2808 q^{71} - 3600 q^{73} + 240 q^{74} - 1800 q^{75} - 2736 q^{76} - 384 q^{77} + 4188 q^{79} + 3168 q^{82} + 4992 q^{83} + 2040 q^{85} + 912 q^{86} - 3312 q^{87} + 3348 q^{89} + 6912 q^{91} - 192 q^{92} - 13356 q^{93} + 4344 q^{94} + 3816 q^{97} + 192 q^{98} + 756 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)