Properties

Label 1110.2.bc
Level $1110$
Weight $2$
Character orbit 1110.bc
Rep. character $\chi_{1110}(181,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $144$
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.bc (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(456\)

Dimensions

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

Total New Old
Modular forms 1416 144 1272
Cusp forms 1320 144 1176
Eisenstein series 96 0 96

Trace form

\( 144q + O(q^{10}) \) \( 144q - 12q^{10} + 12q^{14} + 36q^{19} + 24q^{29} - 72q^{31} + 48q^{33} + 36q^{34} - 24q^{35} + 144q^{36} + 48q^{37} + 48q^{38} + 72q^{39} + 48q^{42} + 96q^{43} - 12q^{44} - 12q^{46} + 24q^{47} - 12q^{55} - 48q^{61} + 48q^{62} - 72q^{64} - 12q^{65} + 96q^{67} - 48q^{68} - 48q^{69} + 72q^{71} + 144q^{73} - 24q^{74} + 36q^{76} + 24q^{77} + 72q^{79} - 48q^{82} - 24q^{83} - 24q^{85} + 24q^{86} - 24q^{87} - 108q^{89} - 12q^{91} - 24q^{92} + 72q^{93} - 36q^{94} + 24q^{97} + 96q^{98} - 12q^{99} + O(q^{100}) \)

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

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