Properties

Label 336.2.bq
Level 336
Weight 2
Character orbit bq
Rep. character \(\chi_{336}(37,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 128
Newforms 2
Sturm bound 128
Trace bound 1

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Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.bq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

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

\( 128q + 4q^{4} + 24q^{8} + O(q^{10}) \) \( 128q + 4q^{4} + 24q^{8} - 12q^{10} + 8q^{11} + 32q^{14} - 4q^{16} - 4q^{18} - 32q^{20} + 32q^{22} - 8q^{28} - 32q^{29} - 48q^{31} + 32q^{34} - 24q^{35} + 16q^{37} - 40q^{38} - 52q^{40} + 20q^{42} + 16q^{43} - 20q^{44} - 20q^{46} + 32q^{48} - 80q^{50} - 24q^{52} - 16q^{53} - 56q^{56} - 8q^{58} + 32q^{59} - 24q^{60} - 144q^{62} - 128q^{64} + 24q^{66} - 32q^{67} - 20q^{68} - 92q^{70} + 4q^{72} + 16q^{74} + 24q^{76} - 72q^{78} + 100q^{80} + 64q^{81} + 20q^{82} + 24q^{84} + 44q^{86} + 48q^{88} + 8q^{91} - 184q^{92} + 60q^{94} - 48q^{95} + 20q^{96} + 124q^{98} - 16q^{99} + O(q^{100}) \)

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.bq.a \(8\) \(2.683\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(8\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{7})q^{2}+\zeta_{24}^{5}q^{3}+(2-2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
336.2.bq.b \(120\) \(2.683\) None \(0\) \(0\) \(-8\) \(0\)

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

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