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Properties

Label 1336.2.j
Level $1336$
Weight $2$
Character orbit 1336.j
Rep. character $\chi_{1336}(35,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $13612$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1336 = 2^{3} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1336.j (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1336 \)
Character field: \(\Q(\zeta_{166})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1336, [\chi])\).

Total New Old
Modular forms 13940 13940 0
Cusp forms 13612 13612 0
Eisenstein series 328 328 0

Trace form

\( 13612 q - 81 q^{2} - 162 q^{3} - 77 q^{4} - 75 q^{6} - 87 q^{8} - 324 q^{9} + O(q^{10}) \) \( 13612 q - 81 q^{2} - 162 q^{3} - 77 q^{4} - 75 q^{6} - 87 q^{8} - 324 q^{9} - 83 q^{10} - 162 q^{11} - 89 q^{12} - 93 q^{14} - 61 q^{16} - 166 q^{17} - 91 q^{18} - 146 q^{19} - 83 q^{20} - 75 q^{22} - 109 q^{24} - 320 q^{25} - 83 q^{26} - 174 q^{27} - 115 q^{28} - 83 q^{30} - 41 q^{32} - 150 q^{33} - 83 q^{34} - 166 q^{35} - 29 q^{36} - 79 q^{38} - 83 q^{40} - 166 q^{41} - 100 q^{42} - 166 q^{43} - 94 q^{44} - 83 q^{46} - 60 q^{48} - 8 q^{49} - 91 q^{50} - 166 q^{51} - 83 q^{52} - 62 q^{54} - 97 q^{56} - 150 q^{57} - 97 q^{58} - 166 q^{59} - 83 q^{60} - 68 q^{62} - 35 q^{64} - 142 q^{65} - 55 q^{66} - 166 q^{67} - 83 q^{68} - 83 q^{70} - 58 q^{72} - 166 q^{73} - 83 q^{74} - 106 q^{75} - 83 q^{76} - 83 q^{78} - 83 q^{80} - 284 q^{81} - 83 q^{82} - 166 q^{83} - 144 q^{84} - 83 q^{86} - 79 q^{88} - 178 q^{89} - 83 q^{90} - 166 q^{91} - 83 q^{92} - 65 q^{94} - 109 q^{96} - 162 q^{97} - 92 q^{98} - 178 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1336, [\chi])\) into newform subspaces

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