Properties

Label 430.2.l
Level 430
Weight 2
Character orbit l
Rep. character \(\chi_{430}(7,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 88
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.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(\zeta_{12})\)
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 280 88 192
Cusp forms 248 88 160
Eisenstein series 32 0 32

Trace form

\( 88q + 4q^{6} + 12q^{7} + O(q^{10}) \) \( 88q + 4q^{6} + 12q^{7} + 16q^{13} - 88q^{16} + 4q^{17} - 16q^{21} + 12q^{23} - 8q^{25} + 12q^{28} - 36q^{30} - 40q^{31} + 12q^{33} - 40q^{35} - 40q^{36} + 16q^{38} - 56q^{41} - 56q^{43} + 24q^{46} + 72q^{47} + 24q^{50} - 16q^{52} + 20q^{53} + 24q^{55} - 8q^{56} + 20q^{57} + 8q^{60} + 72q^{61} + 36q^{62} - 40q^{66} - 16q^{67} + 4q^{68} + 24q^{71} + 60q^{73} - 48q^{76} - 48q^{77} + 40q^{78} + 28q^{81} + 20q^{86} - 64q^{87} - 8q^{90} + 48q^{91} - 12q^{92} - 108q^{93} + 4q^{95} - 4q^{96} - 48q^{97} - 96q^{98} + O(q^{100}) \)

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.l.a \(88\) \(3.434\) None \(0\) \(0\) \(0\) \(12\)

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