Properties

Label 1110.2.br
Level $1110$
Weight $2$
Character orbit 1110.br
Rep. character $\chi_{1110}(151,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $144$
Sturm bound $456$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.br (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{18})\)
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

\( 144q + O(q^{10}) \) \( 144q + 12q^{10} - 36q^{14} - 60q^{19} + 72q^{29} + 48q^{33} + 36q^{34} - 24q^{35} - 144q^{36} + 48q^{37} + 48q^{38} + 24q^{39} + 48q^{42} + 12q^{44} + 12q^{46} + 24q^{47} + 12q^{55} - 48q^{62} + 72q^{64} - 12q^{65} - 24q^{71} + 48q^{73} + 24q^{74} - 60q^{76} + 168q^{77} - 24q^{79} - 24q^{83} - 24q^{85} - 72q^{86} - 24q^{87} - 36q^{89} + 60q^{91} + 24q^{92} - 72q^{93} + 12q^{94} - 72q^{97} - 96q^{98} - 12q^{99} + O(q^{100}) \)

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

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