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Properties

Label 1336.2.c
Level $1336$
Weight $2$
Character orbit 1336.c
Rep. character $\chi_{1336}(669,\cdot)$
Character field $\Q$
Dimension $166$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1336 = 2^{3} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1336.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 170 166 4
Cusp forms 166 166 0
Eisenstein series 4 0 4

Trace form

\( 166 q - 2 q^{2} + 2 q^{4} - 4 q^{7} + 4 q^{8} - 166 q^{9} + O(q^{10}) \) \( 166 q - 2 q^{2} + 2 q^{4} - 4 q^{7} + 4 q^{8} - 166 q^{9} + 6 q^{10} - 10 q^{12} - 14 q^{14} + 10 q^{16} - 4 q^{17} + 20 q^{18} - 6 q^{20} + 4 q^{22} + 8 q^{23} - 2 q^{24} - 162 q^{25} - 4 q^{28} + 12 q^{31} + 18 q^{32} + 8 q^{33} - 2 q^{34} - 10 q^{36} - 16 q^{38} - 4 q^{41} - 13 q^{42} - 11 q^{44} - 8 q^{46} - 4 q^{47} - q^{48} + 150 q^{49} + 28 q^{50} + 36 q^{52} + 3 q^{54} - 18 q^{56} + 8 q^{57} - 18 q^{58} - 4 q^{60} - 25 q^{62} - 20 q^{63} + 8 q^{64} + 16 q^{65} - 16 q^{66} - 24 q^{68} + 48 q^{70} - 8 q^{71} - 27 q^{72} - 4 q^{73} - 22 q^{74} + 24 q^{76} + 74 q^{78} - 40 q^{79} - 16 q^{80} + 174 q^{81} - 10 q^{82} + 7 q^{84} - 26 q^{86} - 24 q^{87} - 36 q^{88} - 20 q^{89} - 14 q^{90} + 36 q^{92} - 14 q^{94} + 24 q^{95} - 22 q^{96} - 4 q^{97} - 21 q^{98} + O(q^{100}) \)

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.