Properties

Label 1336.2.h
Level 1336
Weight 2
Character orbit h
Rep. character \(\chi_{1336}(667,\cdot)\)
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1336 \)
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 170 170 0
Cusp forms 166 166 0
Eisenstein series 4 4 0

Trace form

\( 166q - 2q^{2} - 4q^{3} - 6q^{4} - 8q^{6} + 4q^{8} + 158q^{9} + O(q^{10}) \) \( 166q - 2q^{2} - 4q^{3} - 6q^{4} - 8q^{6} + 4q^{8} + 158q^{9} - 4q^{11} + 6q^{12} + 10q^{14} - 22q^{16} + 8q^{18} - 20q^{19} - 8q^{22} + 26q^{24} + 154q^{25} + 8q^{27} + 32q^{28} - 42q^{32} - 16q^{33} - 54q^{36} - 4q^{38} + 17q^{42} + 11q^{44} - 23q^{48} - 158q^{49} + 8q^{50} - 21q^{54} + 14q^{56} - 16q^{57} + 14q^{58} - 15q^{62} - 48q^{64} - 24q^{65} - 28q^{66} - 25q^{72} - 60q^{75} + 118q^{81} + 61q^{84} - 4q^{88} + 12q^{89} - 18q^{94} + 26q^{96} - 4q^{97} + 9q^{98} + 12q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database