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Properties

Label 2156.2.ci
Level $2156$
Weight $2$
Character orbit 2156.ci
Rep. character $\chi_{2156}(39,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $15936$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2156.ci (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2156 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2156, [\chi])\).

Total New Old
Modular forms 16320 16320 0
Cusp forms 15936 15936 0
Eisenstein series 384 384 0

Trace form

\( 15936 q - 65 q^{2} - 39 q^{4} - 78 q^{5} - 50 q^{6} - 50 q^{8} + 246 q^{9} + O(q^{10}) \) \( 15936 q - 65 q^{2} - 39 q^{4} - 78 q^{5} - 50 q^{6} - 50 q^{8} + 246 q^{9} - 116 q^{12} - 100 q^{13} - 40 q^{14} - 43 q^{16} - 130 q^{17} - 30 q^{18} - 22 q^{20} + 12 q^{22} - 305 q^{24} - 402 q^{25} - 27 q^{26} - 60 q^{28} - 100 q^{29} - 60 q^{30} - 120 q^{33} - 56 q^{34} - 16 q^{36} - 78 q^{37} - 49 q^{38} - 65 q^{40} - 60 q^{41} + 4 q^{42} - 49 q^{44} - 156 q^{45} - 45 q^{46} - 110 q^{48} - 104 q^{49} - 70 q^{50} - 65 q^{52} - 86 q^{53} - 360 q^{56} - 100 q^{57} - 35 q^{58} - 391 q^{60} - 130 q^{61} - 50 q^{62} + 18 q^{64} - q^{66} - 30 q^{68} + 56 q^{69} - 21 q^{70} - 65 q^{72} - 170 q^{73} - 135 q^{74} - 70 q^{77} - 260 q^{78} - 64 q^{80} - 366 q^{81} - 11 q^{82} - 65 q^{84} - 100 q^{85} - 50 q^{86} + 64 q^{88} - 224 q^{89} + 20 q^{90} - 14 q^{92} - 34 q^{93} + 235 q^{94} - 165 q^{96} - 224 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2156, [\chi])\) into newform subspaces

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