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Properties

Label 1656.2.bj
Level $1656$
Weight $2$
Character orbit 1656.bj
Rep. character $\chi_{1656}(19,\cdot)$
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.bj (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

\( 1180 q + 7 q^{2} - 11 q^{4} + 4 q^{8} + O(q^{10}) \) \( 1180 q + 7 q^{2} - 11 q^{4} + 4 q^{8} - 11 q^{10} + 22 q^{11} + 11 q^{14} - 11 q^{16} + 22 q^{17} - 22 q^{19} + 11 q^{20} - 128 q^{25} + 10 q^{26} - 11 q^{28} + 7 q^{32} - 33 q^{34} - 2 q^{35} + 66 q^{38} - 55 q^{40} + 18 q^{41} - 22 q^{43} - 66 q^{44} - 99 q^{46} - 124 q^{49} + 56 q^{50} + 30 q^{52} - 44 q^{56} + 7 q^{58} + 6 q^{59} - 24 q^{62} + 10 q^{64} + 22 q^{65} - 22 q^{67} + 62 q^{70} - 18 q^{73} + 22 q^{74} + 44 q^{76} + 110 q^{80} + 6 q^{82} + 22 q^{83} + 121 q^{86} + 77 q^{88} + 22 q^{89} + 150 q^{92} + 119 q^{94} - 22 q^{97} + 35 q^{98} + O(q^{100}) \)

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

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