Properties

Label 336.2.y
Level 336
Weight 2
Character orbit y
Rep. character \(\chi_{336}(125,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 120
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 336 \)
Character field: \(\Q(i)\)
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 136 136 0
Cusp forms 120 120 0
Eisenstein series 16 16 0

Trace form

\( 120q - 8q^{4} + O(q^{10}) \) \( 120q - 8q^{4} - 8q^{15} + 8q^{16} - 32q^{18} - 8q^{21} + 16q^{22} - 16q^{30} - 8q^{36} - 8q^{37} - 24q^{42} - 8q^{43} - 24q^{46} - 8q^{49} - 56q^{51} + 40q^{58} - 96q^{60} + 24q^{63} - 56q^{64} + 24q^{67} - 80q^{70} - 8q^{72} + 64q^{78} - 16q^{79} - 8q^{81} - 48q^{84} - 48q^{85} - 24q^{88} - 8q^{91} + 8q^{93} - 40q^{99} + O(q^{100}) \)

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.y.a \(120\) \(2.683\) None \(0\) \(0\) \(0\) \(0\)