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Properties

Label 349.2.a
Level $349$
Weight $2$
Character orbit 349.a
Rep. character $\chi_{349}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(349))\) into newform subspaces

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