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Properties

Label 1656.2.cf
Level $1656$
Weight $2$
Character orbit 1656.cf
Rep. character $\chi_{1656}(59,\cdot)$
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.cf (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

\( 5680 q - 27 q^{2} - 36 q^{3} - 9 q^{4} - 11 q^{6} - 36 q^{9} + O(q^{10}) \) \( 5680 q - 27 q^{2} - 36 q^{3} - 9 q^{4} - 11 q^{6} - 36 q^{9} - 44 q^{10} - 54 q^{11} - 30 q^{12} - 27 q^{14} - 9 q^{16} - 11 q^{18} - 72 q^{19} - 27 q^{20} - 12 q^{22} - 52 q^{24} + 250 q^{25} - 24 q^{27} - 20 q^{28} - 20 q^{30} - 27 q^{32} - 24 q^{33} - q^{34} - 69 q^{36} - 75 q^{38} - 53 q^{40} - 54 q^{41} - 24 q^{42} - 18 q^{43} - 56 q^{46} - 36 q^{48} - 278 q^{49} - 135 q^{50} - 60 q^{51} + 16 q^{52} + 12 q^{54} + 15 q^{56} - 12 q^{57} - 26 q^{58} - 90 q^{59} + 38 q^{60} - 30 q^{64} - 54 q^{65} + 19 q^{66} - 18 q^{67} - 6 q^{68} - 58 q^{70} - 20 q^{72} - 72 q^{73} + 45 q^{74} - 68 q^{75} + 11 q^{76} + 197 q^{78} - 52 q^{81} - 46 q^{82} - 54 q^{83} + 142 q^{84} - 27 q^{86} - 25 q^{88} - 290 q^{90} - 104 q^{91} - 117 q^{92} + 18 q^{94} + 70 q^{96} - 18 q^{97} + O(q^{100}) \)

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.