Properties

Label 336.2.bs
Level 336
Weight 2
Character orbit bs
Rep. character \(\chi_{336}(19,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 128
Newforms 1
Sturm bound 128
Trace bound 0

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Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.bs (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).

Total New Old
Modular forms 272 128 144
Cusp forms 240 128 112
Eisenstein series 32 0 32

Trace form

\( 128q + 4q^{4} - 24q^{8} + O(q^{10}) \) \( 128q + 4q^{4} - 24q^{8} + 36q^{10} - 8q^{11} - 32q^{14} - 4q^{16} + 4q^{18} + 16q^{22} + 16q^{23} - 32q^{28} + 32q^{29} - 24q^{35} - 16q^{37} + 60q^{40} - 20q^{42} - 16q^{43} - 12q^{44} - 20q^{46} - 32q^{50} - 144q^{52} - 16q^{53} - 56q^{56} - 40q^{58} - 96q^{59} - 24q^{60} - 32q^{64} - 72q^{66} + 16q^{67} - 60q^{68} + 28q^{70} + 128q^{71} - 4q^{72} - 72q^{74} + 72q^{78} - 36q^{80} + 64q^{81} - 60q^{82} + 24q^{84} - 44q^{86} - 48q^{88} - 8q^{91} + 56q^{92} + 36q^{94} + 60q^{96} + 148q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
336.2.bs.a \(128\) \(2.683\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)