Properties

Label 336.2.bu
Level 336
Weight 2
Character orbit bu
Rep. character \(\chi_{336}(11,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 240
Newform subspaces 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.bu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
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

\( 240q - 2q^{3} - 4q^{4} - 8q^{6} - 16q^{7} + O(q^{10}) \) \( 240q - 2q^{3} - 4q^{4} - 8q^{6} - 16q^{7} - 4q^{10} - 2q^{12} - 16q^{13} - 20q^{16} + 16q^{18} - 4q^{19} + 2q^{21} - 40q^{22} - 22q^{24} - 8q^{27} - 4q^{28} - 26q^{30} - 4q^{33} + 16q^{36} - 4q^{37} - 4q^{39} + 8q^{40} - 18q^{42} - 16q^{43} + 18q^{45} - 20q^{46} - 88q^{48} - 16q^{49} + 6q^{51} + 8q^{52} + 14q^{54} - 32q^{55} - 36q^{58} - 42q^{60} - 4q^{61} - 64q^{64} - 30q^{66} - 36q^{67} - 20q^{69} + 116q^{70} - 46q^{72} - 24q^{75} - 112q^{76} - 92q^{78} - 4q^{81} - 32q^{82} + 44q^{84} - 56q^{85} - 4q^{87} - 20q^{88} + 28q^{90} - 40q^{91} - 14q^{93} + 72q^{94} + 36q^{96} - 32q^{97} + 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
336.2.bu.a \(240\) \(2.683\) None \(0\) \(-2\) \(0\) \(-16\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database