Properties

Label 350.2.u
Level 350
Weight 2
Character orbit u
Rep. character \(\chi_{350}(9,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 160
Newform subspaces 1
Sturm bound 120
Trace bound 0

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Defining parameters

Level: \( N \) = \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 350.u (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(350, [\chi])\).

Total New Old
Modular forms 512 160 352
Cusp forms 448 160 288
Eisenstein series 64 0 64

Trace form

\( 160q - 20q^{4} - 2q^{5} + 8q^{6} - 20q^{9} + O(q^{10}) \) \( 160q - 20q^{4} - 2q^{5} + 8q^{6} - 20q^{9} - 2q^{10} - 6q^{11} - 16q^{15} + 20q^{16} - 20q^{17} + 4q^{19} - 4q^{20} - 12q^{21} + 40q^{22} - 30q^{23} - 16q^{24} + 48q^{26} - 120q^{27} - 10q^{28} + 24q^{29} - 26q^{30} - 6q^{31} - 50q^{33} - 16q^{34} - 36q^{35} - 40q^{36} - 32q^{39} + 2q^{40} + 68q^{41} + 10q^{42} - 4q^{44} + 16q^{45} + 12q^{46} + 24q^{49} + 32q^{50} + 12q^{51} - 20q^{53} + 16q^{54} + 24q^{55} + 24q^{59} + 2q^{60} - 8q^{61} + 40q^{64} + 2q^{65} - 116q^{69} - 118q^{70} + 68q^{71} - 40q^{73} + 16q^{74} + 196q^{75} - 32q^{76} - 80q^{77} - 8q^{79} - 2q^{80} + 64q^{81} - 160q^{83} - 18q^{84} + 12q^{85} + 12q^{86} - 10q^{88} + 54q^{89} + 44q^{91} - 40q^{92} - 16q^{95} - 4q^{96} - 20q^{97} + 40q^{98} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
350.2.u.a \(160\) \(2.795\) None \(0\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database