Properties

Label 353.2.d
Level $353$
Weight $2$
Character orbit 353.d
Rep. character $\chi_{353}(70,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $112$
Newform subspaces $1$
Sturm bound $59$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 353 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 353.d (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 353 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(59\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(353, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 112 112 0
Eisenstein series 8 8 0

Trace form

\( 112q - 112q^{4} - 4q^{5} + 8q^{6} - 4q^{7} + 4q^{9} + O(q^{10}) \) \( 112q - 112q^{4} - 4q^{5} + 8q^{6} - 4q^{7} + 4q^{9} - 4q^{10} - 16q^{12} + 16q^{13} + 24q^{14} + 96q^{16} - 12q^{18} - 4q^{19} - 24q^{22} - 24q^{23} - 20q^{24} - 44q^{25} + 8q^{26} + 24q^{27} - 44q^{28} + 44q^{30} + 4q^{31} - 36q^{33} + 24q^{35} + 20q^{36} - 4q^{37} + 32q^{38} + 8q^{39} - 32q^{40} - 32q^{41} + 56q^{42} - 48q^{43} - 104q^{45} + 76q^{46} - 44q^{47} + 4q^{48} + 8q^{49} + 20q^{50} - 32q^{51} - 72q^{52} + 20q^{53} + 64q^{54} + 16q^{55} - 24q^{56} - 20q^{57} - 64q^{58} + 60q^{59} - 176q^{60} - 12q^{62} + 28q^{63} - 104q^{64} + 4q^{65} + 64q^{66} + 8q^{67} - 48q^{69} + 8q^{71} + 56q^{72} + 4q^{74} + 92q^{75} - 20q^{77} + 72q^{78} + 24q^{79} - 36q^{80} - 72q^{82} - 4q^{85} - 44q^{86} + 24q^{87} + 344q^{88} + 16q^{89} - 44q^{90} + 44q^{92} + 76q^{93} + 148q^{94} - 20q^{95} + 4q^{96} + 72q^{97} - 64q^{98} + 56q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(353, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
353.2.d.a \(112\) \(2.819\) None \(0\) \(0\) \(-4\) \(-4\)