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Properties

Label 1110.2.bz
Level $1110$
Weight $2$
Character orbit 1110.bz
Rep. character $\chi_{1110}(131,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $624$
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.bz (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(456\)

Dimensions

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

Total New Old
Modular forms 2832 624 2208
Cusp forms 2640 624 2016
Eisenstein series 192 0 192

Trace form

\( 624 q + O(q^{10}) \) \( 624 q + 72 q^{21} - 48 q^{28} + 24 q^{31} + 120 q^{34} + 48 q^{37} + 96 q^{43} + 48 q^{45} + 96 q^{49} - 72 q^{54} + 72 q^{57} - 48 q^{61} + 72 q^{63} + 168 q^{69} + 96 q^{78} + 48 q^{79} + 96 q^{81} + 48 q^{82} + 144 q^{87} + 192 q^{91} - 144 q^{93} - 144 q^{94} - 48 q^{97} - 72 q^{99} + O(q^{100}) \)

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

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