Properties

Label 430.2.r
Level 430
Weight 2
Character orbit r
Rep. character \(\chi_{430}(27,\cdot)\)
Character field \(\Q(\zeta_{28})\)
Dimension 264
Newform subspaces 1
Sturm bound 132
Trace bound 0

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Defining parameters

Level: \( N \) = \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 430.r (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(430, [\chi])\).

Total New Old
Modular forms 840 264 576
Cusp forms 744 264 480
Eisenstein series 96 0 96

Trace form

\( 264q - 8q^{6} + O(q^{10}) \) \( 264q - 8q^{6} - 40q^{13} + 44q^{16} - 8q^{17} - 16q^{21} - 24q^{23} - 8q^{25} + 48q^{31} - 56q^{33} + 32q^{35} + 256q^{36} - 100q^{38} + 40q^{41} - 168q^{43} + 48q^{47} - 280q^{51} - 16q^{52} + 24q^{53} - 8q^{56} - 40q^{57} - 16q^{60} - 84q^{62} + 84q^{65} + 144q^{66} + 40q^{67} + 20q^{68} - 252q^{73} - 56q^{77} - 56q^{78} + 48q^{81} - 56q^{82} - 44q^{83} + 20q^{86} - 144q^{87} + 4q^{90} + 24q^{92} + 28q^{95} + 8q^{96} - 60q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(430, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
430.2.r.a \(264\) \(3.434\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(430, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(430, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(215, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database