Properties

Label 1110.2.bp
Level $1110$
Weight $2$
Character orbit 1110.bp
Rep. character $\chi_{1110}(139,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $216$
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.bp (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
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 216 1200
Cusp forms 1320 216 1104
Eisenstein series 96 0 96

Trace form

\( 216q - 6q^{5} + O(q^{10}) \) \( 216q - 6q^{5} - 36q^{14} - 12q^{19} + 6q^{20} - 24q^{21} + 30q^{25} + 36q^{26} - 24q^{30} - 48q^{34} - 48q^{35} - 216q^{36} - 48q^{39} - 12q^{40} + 180q^{41} + 12q^{44} + 36q^{46} + 24q^{49} - 84q^{50} + 12q^{55} - 96q^{61} - 108q^{64} + 90q^{65} - 24q^{69} + 12q^{70} + 48q^{71} + 84q^{74} + 12q^{76} + 72q^{79} - 24q^{84} - 18q^{85} + 72q^{86} + 108q^{89} - 6q^{90} - 180q^{91} + 12q^{94} + 60q^{95} - 12q^{99} + O(q^{100}) \)

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

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