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Properties

Label 1170.2.cl
Level $1170$
Weight $2$
Character orbit 1170.cl
Rep. character $\chi_{1170}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.cl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

Total New Old
Modular forms 1072 112 960
Cusp forms 944 112 832
Eisenstein series 128 0 128

Trace form

\( 112 q + O(q^{10}) \) \( 112 q - 36 q^{13} + 56 q^{16} - 12 q^{37} - 8 q^{40} - 16 q^{43} + 48 q^{46} + 24 q^{52} - 16 q^{55} + 12 q^{58} - 96 q^{61} + 48 q^{67} + 96 q^{76} - 36 q^{82} + 12 q^{85} - 48 q^{91} - 144 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)