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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1336, [\chi])\) into irreducible Hecke orbits

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