Properties

Label 350.2.x
Level 350
Weight 2
Character orbit x
Rep. character \(\chi_{350}(3,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 320
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.x (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{60})\)
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 1024 320 704
Cusp forms 896 320 576
Eisenstein series 128 0 128

Trace form

\( 320q + 12q^{5} - 8q^{7} + O(q^{10}) \) \( 320q + 12q^{5} - 8q^{7} + 12q^{10} - 16q^{15} - 40q^{16} + 36q^{17} + 8q^{18} - 72q^{22} + 44q^{23} - 12q^{25} - 24q^{28} - 80q^{29} + 20q^{30} - 48q^{33} - 28q^{35} + 80q^{36} - 4q^{37} - 24q^{38} - 40q^{39} - 36q^{42} + 88q^{43} - 228q^{45} - 12q^{47} + 32q^{50} - 52q^{53} + 152q^{57} + 32q^{58} - 120q^{59} - 8q^{60} + 136q^{63} + 8q^{65} - 32q^{67} - 144q^{68} + 92q^{70} + 8q^{72} + 12q^{73} - 432q^{75} + 144q^{77} - 16q^{78} + 12q^{80} - 40q^{81} - 192q^{82} + 60q^{84} - 24q^{85} + 24q^{87} + 4q^{88} - 300q^{89} - 8q^{92} - 68q^{93} + 20q^{95} - 40q^{98} + O(q^{100}) \)

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.x.a \(320\) \(2.795\) None \(0\) \(0\) \(12\) \(-8\)

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