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Properties

Label 2156.2.cg
Level $2156$
Weight $2$
Character orbit 2156.cg
Rep. character $\chi_{2156}(3,\cdot)$
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.cg (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

\( 15936 q - 39 q^{2} - 39 q^{4} - 66 q^{5} - 42 q^{6} - 30 q^{8} - 402 q^{9} + O(q^{10}) \) \( 15936 q - 39 q^{2} - 39 q^{4} - 66 q^{5} - 42 q^{6} - 30 q^{8} - 402 q^{9} - 88 q^{10} - 88 q^{12} - 84 q^{13} - 32 q^{14} - 35 q^{16} - 66 q^{17} - 16 q^{18} - 42 q^{20} - 180 q^{21} - 92 q^{22} - 87 q^{24} + 246 q^{25} - 21 q^{26} + 28 q^{28} - 60 q^{29} - 22 q^{30} - 104 q^{32} - 76 q^{33} - 224 q^{34} - 52 q^{36} - 78 q^{37} - 31 q^{38} - 63 q^{40} - 84 q^{41} - 128 q^{42} - 49 q^{44} - 140 q^{45} - 27 q^{46} - 56 q^{49} - 34 q^{50} + 27 q^{52} - 86 q^{53} - 106 q^{54} + 168 q^{56} - 120 q^{57} - 43 q^{58} + 329 q^{60} - 90 q^{61} - 70 q^{62} + 66 q^{64} - 196 q^{65} + 81 q^{66} + 12 q^{68} - 196 q^{69} - 137 q^{70} - 65 q^{72} - 66 q^{73} + 33 q^{74} - 168 q^{76} - 122 q^{77} - 252 q^{78} - 54 q^{80} - 390 q^{81} - 93 q^{82} - 367 q^{84} - 52 q^{85} - 20 q^{86} - 192 q^{88} - 176 q^{89} - 70 q^{90} - 98 q^{92} - 122 q^{93} + 111 q^{94} + 93 q^{96} - 560 q^{98} + O(q^{100}) \)

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.