Properties

Label 430.2.j
Level 430
Weight 2
Character orbit j
Rep. character \(\chi_{430}(49,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 44
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(\zeta_{6})\)
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 140 44 96
Cusp forms 124 44 80
Eisenstein series 16 0 16

Trace form

\( 44q - 44q^{4} - 4q^{5} + 2q^{6} + 20q^{9} + O(q^{10}) \) \( 44q - 44q^{4} - 4q^{5} + 2q^{6} + 20q^{9} + 8q^{11} + 4q^{14} - 4q^{15} + 44q^{16} - 4q^{19} + 4q^{20} - 24q^{21} - 2q^{24} + 12q^{26} - 10q^{29} - 20q^{31} - 12q^{34} + 12q^{35} - 20q^{36} + 120q^{39} + 20q^{41} - 8q^{44} - 28q^{45} + 42q^{49} - 112q^{51} - 68q^{54} - 26q^{55} - 4q^{56} + 40q^{59} + 4q^{60} + 8q^{61} - 44q^{64} - 60q^{65} - 12q^{66} - 4q^{69} + 48q^{70} - 20q^{71} - 12q^{74} + 4q^{75} + 4q^{76} - 44q^{79} - 4q^{80} + 2q^{81} + 24q^{84} + 20q^{85} + 14q^{86} - 26q^{89} + 68q^{90} + 4q^{94} - 34q^{95} + 2q^{96} + 72q^{99} + O(q^{100}) \)

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.j.a \(44\) \(3.434\) None \(0\) \(0\) \(-4\) \(0\)

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