Properties

Label 350.2.r
Level 350
Weight 2
Character orbit r
Rep. character \(\chi_{350}(13,\cdot)\)
Character field \(\Q(\zeta_{20})\)
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.r (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 160q + 8q^{7} + O(q^{10}) \) \( 160q + 8q^{7} + 16q^{15} + 40q^{16} - 8q^{18} - 24q^{22} - 32q^{23} + 12q^{28} - 40q^{29} - 56q^{30} + 28q^{35} + 40q^{36} - 32q^{37} + 40q^{39} - 112q^{43} - 32q^{50} + 112q^{53} - 152q^{57} + 16q^{58} + 8q^{60} - 100q^{63} - 8q^{65} - 16q^{67} - 56q^{70} - 8q^{72} - 144q^{77} + 40q^{78} + 40q^{81} - 60q^{84} + 48q^{85} - 16q^{88} + 8q^{92} + 56q^{93} - 104q^{95} - 32q^{98} + O(q^{100}) \)

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.r.a \(160\) \(2.795\) None \(0\) \(0\) \(0\) \(8\)

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