Properties

Label 353.2.a
Level $353$
Weight $2$
Character orbit 353.a
Rep. character $\chi_{353}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $4$
Sturm bound $59$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 353 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 353.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(59\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(353))\).

Total New Old
Modular forms 30 30 0
Cusp forms 29 29 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.

\(353\)Dim.
\(+\)\(11\)
\(-\)\(18\)

Trace form

\( 29q - q^{2} - 2q^{3} + 27q^{4} - 4q^{5} - 6q^{6} + 4q^{7} - 3q^{8} + 23q^{9} + O(q^{10}) \) \( 29q - q^{2} - 2q^{3} + 27q^{4} - 4q^{5} - 6q^{6} + 4q^{7} - 3q^{8} + 23q^{9} - 6q^{10} - 4q^{11} - 22q^{12} + 2q^{13} + 8q^{14} - 2q^{15} + 27q^{16} - 6q^{17} - 7q^{18} + 2q^{20} + 2q^{21} + 6q^{22} - 10q^{23} + 19q^{25} + 12q^{26} - 8q^{27} + 18q^{28} + 6q^{29} + 2q^{30} + 2q^{31} + 3q^{32} - 18q^{33} - 26q^{34} - 4q^{35} + 27q^{36} + 6q^{37} + 12q^{38} - 30q^{39} - 36q^{40} - 10q^{41} - 20q^{42} - 14q^{43} - 10q^{44} - 44q^{45} - 2q^{46} - 10q^{47} - 60q^{48} + 59q^{49} - 3q^{50} - 22q^{51} - 2q^{52} - 8q^{53} - 40q^{54} + 4q^{55} + 58q^{56} + 28q^{57} - 16q^{58} - 2q^{59} + 16q^{61} + 14q^{62} + 24q^{63} + 5q^{64} - 8q^{65} + 24q^{66} + 24q^{67} - 20q^{68} - 10q^{69} - 24q^{70} + 10q^{71} + 21q^{72} + 10q^{73} - 2q^{74} + 46q^{75} - 12q^{76} - 32q^{77} + 6q^{78} + 12q^{79} - 12q^{80} + 21q^{81} - 18q^{82} - 8q^{83} - 44q^{84} - 52q^{85} - 16q^{86} + 24q^{87} - 22q^{88} - 2q^{89} - 40q^{90} + 46q^{91} + 34q^{92} - 20q^{93} - 16q^{94} - 12q^{95} - 18q^{96} - 8q^{97} - 81q^{98} - 38q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(353))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 353
353.2.a.a \(1\) \(2.819\) \(\Q\) None \(-1\) \(2\) \(2\) \(-2\) \(-\) \(q-q^{2}+2q^{3}-q^{4}+2q^{5}-2q^{6}-2q^{7}+\cdots\)
353.2.a.b \(3\) \(2.819\) 3.3.229.1 None \(1\) \(3\) \(2\) \(2\) \(-\) \(q+(\beta _{1}-\beta _{2})q^{2}+(1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
353.2.a.c \(11\) \(2.819\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-5\) \(-5\) \(-4\) \(-25\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2}-\beta _{5}-\beta _{8}+\cdots)q^{3}+\cdots\)
353.2.a.d \(14\) \(2.819\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(4\) \(-2\) \(-4\) \(29\) \(-\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)