Properties

Label 349.2.b
Level 349
Weight 2
Character orbit b
Rep. character \(\chi_{349}(348,\cdot)\)
Character field \(\Q\)
Dimension 28
Newforms 2
Sturm bound 58
Trace bound 1

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Defining parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 349 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(58\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(349, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 28 28 0
Eisenstein series 2 2 0

Trace form

\( 28q - 4q^{3} - 32q^{4} - 8q^{5} + 28q^{9} + O(q^{10}) \) \( 28q - 4q^{3} - 32q^{4} - 8q^{5} + 28q^{9} + 8q^{12} + 4q^{14} + 8q^{15} + 28q^{16} - 8q^{17} - 14q^{19} + 6q^{20} - 12q^{22} - 16q^{23} + 16q^{25} + 22q^{26} + 14q^{27} - 16q^{29} + 24q^{31} - 62q^{36} + 24q^{37} + 4q^{41} - 52q^{45} - 82q^{48} - 48q^{49} + 26q^{51} - 38q^{56} - 6q^{57} - 86q^{60} - 80q^{64} + 104q^{66} + 46q^{67} + 48q^{68} - 42q^{69} + 86q^{70} + 50q^{73} - 36q^{75} + 76q^{76} - 68q^{77} - 30q^{78} + 46q^{80} - 4q^{81} - 6q^{83} - 10q^{85} + 60q^{86} + 30q^{87} + 110q^{88} + 28q^{91} + 18q^{92} + 70q^{93} + 22q^{94} - 30q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(349, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
349.2.b.a \(2\) \(2.787\) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(4\) \(0\) \(q-q^{3}+2q^{4}+2q^{5}+\beta q^{7}-2q^{9}+\cdots\)
349.2.b.b \(26\) \(2.787\) None \(0\) \(-2\) \(-12\) \(0\)