Properties

Label 336.2.w
Level 336
Weight 2
Character orbit w
Rep. character \(\chi_{336}(85,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 48
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 16 \)
Character field: \(\Q(i)\)
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 136 48 88
Cusp forms 120 48 72
Eisenstein series 16 0 16

Trace form

\( 48q + 4q^{4} + O(q^{10}) \) \( 48q + 4q^{4} - 8q^{10} + 8q^{11} - 16q^{12} + 4q^{14} + 16q^{15} + 4q^{16} - 4q^{18} + 16q^{19} - 20q^{22} - 8q^{24} - 40q^{26} + 16q^{29} + 16q^{30} - 32q^{34} + 8q^{36} + 16q^{37} + 56q^{38} - 40q^{40} + 24q^{43} + 52q^{44} - 24q^{46} - 48q^{49} + 68q^{50} - 16q^{51} - 16q^{52} - 16q^{53} - 8q^{54} - 28q^{56} + 4q^{58} - 24q^{60} - 32q^{61} - 48q^{62} - 8q^{63} + 28q^{64} + 32q^{65} - 8q^{67} - 104q^{68} - 32q^{69} - 24q^{70} + 4q^{72} + 12q^{74} - 32q^{75} - 40q^{76} - 16q^{77} + 24q^{78} + 48q^{79} - 80q^{80} - 48q^{81} - 40q^{82} + 80q^{83} + 32q^{85} - 60q^{86} + 20q^{88} + 16q^{90} + 48q^{92} - 40q^{94} + 40q^{96} + 8q^{99} + O(q^{100}) \)

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.w.a \(20\) \(2.683\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-\beta _{7}q^{3}+(\beta _{1}-\beta _{3}-\beta _{6}-\beta _{16}+\cdots)q^{4}+\cdots\)
336.2.w.b \(28\) \(2.683\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)