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Properties

Label 1110.2.bf
Level $1110$
Weight $2$
Character orbit 1110.bf
Rep. character $\chi_{1110}(97,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $152$
Sturm bound $456$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1110, [\chi])\).

Total New Old
Modular forms 944 152 792
Cusp forms 880 152 728
Eisenstein series 64 0 64

Trace form

\( 152 q - 4 q^{2} - 76 q^{4} - 4 q^{5} + 8 q^{8} + O(q^{10}) \) \( 152 q - 4 q^{2} - 76 q^{4} - 4 q^{5} + 8 q^{8} + 4 q^{10} - 16 q^{14} - 76 q^{16} + 8 q^{19} + 8 q^{20} + 4 q^{25} - 16 q^{26} + 36 q^{29} + 24 q^{30} - 4 q^{32} + 80 q^{35} - 12 q^{37} + 32 q^{39} + 4 q^{40} - 60 q^{41} + 32 q^{43} + 24 q^{44} - 96 q^{49} + 72 q^{50} - 16 q^{51} + 60 q^{53} + 16 q^{55} + 8 q^{56} - 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 16 q^{62} + 152 q^{64} - 24 q^{65} + 8 q^{66} - 16 q^{67} - 16 q^{69} - 8 q^{70} + 16 q^{71} - 8 q^{73} - 40 q^{74} - 32 q^{75} + 32 q^{76} + 56 q^{77} + 24 q^{79} - 4 q^{80} + 76 q^{81} - 24 q^{83} + 16 q^{86} - 36 q^{89} + 40 q^{91} - 8 q^{93} + 32 q^{94} - 72 q^{95} + 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

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