Properties

Label 336.2.bo
Level 336
Weight 2
Character orbit bo
Rep. character \(\chi_{336}(5,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 240
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.bo (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 336 \)
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 272 272 0
Cusp forms 240 240 0
Eisenstein series 32 32 0

Trace form

\( 240q - 6q^{3} - 4q^{4} + O(q^{10}) \) \( 240q - 6q^{3} - 4q^{4} - 12q^{10} - 6q^{12} - 16q^{15} - 20q^{16} - 4q^{18} - 12q^{19} + 2q^{21} - 40q^{22} - 6q^{24} - 12q^{28} + 22q^{30} - 24q^{31} - 12q^{33} - 64q^{36} - 4q^{37} + 48q^{40} - 18q^{42} - 16q^{43} - 6q^{45} + 12q^{46} - 16q^{49} - 10q^{51} - 48q^{52} - 90q^{54} - 4q^{58} - 18q^{60} - 12q^{61} - 36q^{63} + 32q^{64} - 66q^{66} - 36q^{67} - 76q^{70} - 46q^{72} + 24q^{75} - 76q^{78} - 8q^{79} - 4q^{81} + 72q^{82} - 24q^{84} + 24q^{85} + 12q^{88} - 88q^{91} - 14q^{93} + 24q^{94} + 96q^{96} + 28q^{99} + O(q^{100}) \)

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.bo.a \(240\) \(2.683\) None \(0\) \(-6\) \(0\) \(0\)