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Properties

Label 1656.2.cj
Level $1656$
Weight $2$
Character orbit 1656.cj
Rep. character $\chi_{1656}(43,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $5680$
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.cj (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1656 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 5840 5840 0
Cusp forms 5680 5680 0
Eisenstein series 160 160 0

Trace form

\( 5680 q - 9 q^{2} - 36 q^{3} - 9 q^{4} - 19 q^{6} - 42 q^{8} - 36 q^{9} + O(q^{10}) \) \( 5680 q - 9 q^{2} - 36 q^{3} - 9 q^{4} - 19 q^{6} - 42 q^{8} - 36 q^{9} - 44 q^{10} - 22 q^{11} - 30 q^{12} - 11 q^{14} - 9 q^{16} - 88 q^{17} - 25 q^{18} - 88 q^{19} - 11 q^{20} - 28 q^{24} + 250 q^{25} - 16 q^{26} - 24 q^{27} - 44 q^{28} - 22 q^{30} - 9 q^{32} - 44 q^{33} - 11 q^{34} - 112 q^{35} - 69 q^{36} - 11 q^{38} + 55 q^{40} - 18 q^{41} - 22 q^{42} - 22 q^{43} - 44 q^{44} - 48 q^{46} - 24 q^{48} + 242 q^{49} - 33 q^{50} - 44 q^{51} - 2 q^{52} - 48 q^{54} - 11 q^{56} - 44 q^{57} + 8 q^{58} - 6 q^{59} - 22 q^{60} - 22 q^{62} - 30 q^{64} - 22 q^{65} - 55 q^{66} - 22 q^{67} - 22 q^{70} - 68 q^{72} - 72 q^{73} - 11 q^{74} - 68 q^{75} - 11 q^{76} + 49 q^{78} - 44 q^{80} - 52 q^{81} - 26 q^{82} - 22 q^{83} - 176 q^{84} - 11 q^{86} - 11 q^{88} - 88 q^{89} + 418 q^{90} - 3 q^{92} - 36 q^{94} - 210 q^{96} - 22 q^{97} - 140 q^{98} - 44 q^{99} + O(q^{100}) \)

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.