Properties

Label 336.2.u
Level 336
Weight 2
Character orbit u
Rep. character \(\chi_{336}(139,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 64
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 112 \)
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 64 72
Cusp forms 120 64 56
Eisenstein series 16 0 16

Trace form

\( 64q - 4q^{4} + 24q^{8} + O(q^{10}) \) \( 64q - 4q^{4} + 24q^{8} + 8q^{11} - 16q^{14} + 4q^{16} - 4q^{18} - 28q^{22} - 16q^{23} + 32q^{28} + 16q^{29} + 24q^{35} + 16q^{37} + 20q^{42} - 8q^{43} - 36q^{44} - 40q^{46} - 52q^{50} + 16q^{53} - 28q^{56} - 92q^{58} + 24q^{60} - 52q^{64} + 56q^{67} - 40q^{70} - 128q^{71} + 4q^{72} - 60q^{74} - 64q^{81} - 24q^{84} + 92q^{86} - 84q^{88} + 8q^{91} + 136q^{92} - 64q^{98} - 8q^{99} + O(q^{100}) \)

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.u.a \(64\) \(2.683\) None \(0\) \(0\) \(0\) \(0\)

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

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