Properties

Label 349.2.a
Level 349
Weight 2
Character orbit a
Rep. character \(\chi_{349}(1,\cdot)\)
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.a (trivial)
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 \(M_{2}(\Gamma_0(349))\).

Total New Old
Modular forms 29 29 0
Cusp forms 28 28 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(349\)Dim.
\(+\)\(11\)
\(-\)\(17\)

Trace form

\( 28q + 24q^{4} - 4q^{5} - 8q^{6} - 2q^{7} - 6q^{8} + 28q^{9} + O(q^{10}) \) \( 28q + 24q^{4} - 4q^{5} - 8q^{6} - 2q^{7} - 6q^{8} + 28q^{9} - 4q^{10} + 8q^{11} + 4q^{12} - 10q^{13} + 4q^{14} + 28q^{16} - 10q^{19} - 2q^{20} - 18q^{21} + 16q^{22} - 16q^{23} - 24q^{24} + 24q^{25} - 10q^{26} - 6q^{27} - 20q^{28} - 8q^{29} - 18q^{30} - 12q^{31} + 18q^{32} + 6q^{33} - 10q^{34} - 12q^{35} + 6q^{36} - 8q^{37} - 6q^{38} + 8q^{39} - 18q^{40} - 12q^{41} - 4q^{43} + 32q^{44} - 24q^{45} + 22q^{46} + 20q^{47} - 2q^{48} + 20q^{49} - 8q^{50} + 10q^{51} - 12q^{52} + 24q^{53} - 8q^{54} + 8q^{55} + 22q^{56} - 10q^{57} - 36q^{58} + 22q^{59} - 6q^{60} - 30q^{61} + 24q^{62} + 26q^{63} - 12q^{64} - 6q^{65} - 36q^{66} - 14q^{67} - 36q^{68} + 2q^{69} - 50q^{70} + 40q^{71} - 32q^{72} - 26q^{73} + 56q^{74} + 56q^{75} - 48q^{76} - 32q^{77} - 34q^{78} + 18q^{79} - 10q^{80} + 12q^{81} - 10q^{82} + 34q^{83} - 46q^{84} - 30q^{85} - 4q^{86} - 2q^{87} + 50q^{88} + 4q^{89} - 26q^{90} - 24q^{91} + 18q^{92} - 18q^{93} - 42q^{94} - 18q^{95} - 36q^{96} + 12q^{97} + 40q^{98} + 38q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(349))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 349
349.2.a.a \(11\) \(2.787\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-5\) \(-6\) \(-9\) \(-3\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{3}+\cdots\)
349.2.a.b \(17\) \(2.787\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(5\) \(6\) \(5\) \(1\) \(-\) \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)