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Properties

Label 1656.2.br
Level $1656$
Weight $2$
Character orbit 1656.br
Rep. character $\chi_{1656}(325,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1180$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1656.br (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1656, [\chi])\).

Total New Old
Modular forms 2960 1220 1740
Cusp forms 2800 1180 1620
Eisenstein series 160 40 120

Trace form

\( 1180 q + 7 q^{2} - 3 q^{4} - 22 q^{7} + 10 q^{8} + O(q^{10}) \) \( 1180 q + 7 q^{2} - 3 q^{4} - 22 q^{7} + 10 q^{8} - 17 q^{10} + 7 q^{14} - 11 q^{16} + 18 q^{17} + 7 q^{20} - 34 q^{22} + 24 q^{23} + 92 q^{25} + 16 q^{26} + 23 q^{28} - 2 q^{31} + 7 q^{32} - 11 q^{34} - 12 q^{38} - 9 q^{40} + 18 q^{41} + 82 q^{44} + 85 q^{46} + 40 q^{47} - 124 q^{49} - 82 q^{50} - 114 q^{52} - 38 q^{55} + 16 q^{56} - 15 q^{58} + 22 q^{62} - 6 q^{64} + 38 q^{65} + 34 q^{68} + 34 q^{70} + 10 q^{71} - 18 q^{73} - 20 q^{74} + 40 q^{76} - 22 q^{79} + 104 q^{80} + 72 q^{82} + 95 q^{86} + 89 q^{88} + 2 q^{89} + 110 q^{92} + 17 q^{94} - 2 q^{95} - 18 q^{97} + 23 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1656, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1656, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1656, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)