Properties

Label 1110.2.be
Level $1110$
Weight $2$
Character orbit 1110.be
Rep. character $\chi_{1110}(251,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $192$
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.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
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 944 192 752
Cusp forms 880 192 688
Eisenstein series 64 0 64

Trace form

\( 192q + O(q^{10}) \) \( 192q + 24q^{13} + 96q^{16} - 24q^{19} - 72q^{21} + 72q^{28} + 24q^{31} + 8q^{34} + 96q^{37} - 32q^{39} + 24q^{42} - 8q^{43} - 32q^{45} - 40q^{49} - 8q^{51} - 24q^{52} + 72q^{54} - 24q^{55} - 24q^{57} + 88q^{61} + 144q^{63} + 48q^{66} - 8q^{69} + 24q^{76} - 96q^{78} - 80q^{79} + 16q^{81} - 16q^{82} + 24q^{87} - 216q^{91} + 16q^{93} + 64q^{94} + 88q^{97} + 72q^{99} + O(q^{100}) \)

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

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