Properties

Label 430.2.t
Level 430
Weight 2
Character orbit t
Rep. character \(\chi_{430}(9,\cdot)\)
Character field \(\Q(\zeta_{42})\)
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.t (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(\zeta_{42})\)
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

\( 264q + 44q^{4} + 4q^{5} - 2q^{6} - 6q^{9} + O(q^{10}) \) \( 264q + 44q^{4} + 4q^{5} - 2q^{6} - 6q^{9} - 8q^{11} + 10q^{14} + 32q^{15} - 44q^{16} + 4q^{19} - 4q^{20} + 24q^{21} + 2q^{24} + 28q^{25} - 12q^{26} - 46q^{29} - 36q^{31} + 12q^{34} - 68q^{35} - 134q^{36} - 64q^{39} - 20q^{41} + 8q^{44} - 70q^{45} + 112q^{49} - 28q^{50} - 28q^{51} + 68q^{54} - 30q^{55} + 4q^{56} - 40q^{59} - 4q^{60} + 20q^{61} + 44q^{64} + 18q^{65} - 44q^{66} + 32q^{69} - 48q^{70} + 20q^{71} + 40q^{74} + 122q^{75} + 52q^{76} + 16q^{79} + 4q^{80} - 16q^{81} - 24q^{84} + 120q^{85} - 14q^{86} - 142q^{89} - 68q^{90} - 4q^{94} - 22q^{95} - 2q^{96} - 268q^{99} + O(q^{100}) \)

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.t.a \(264\) \(3.434\) 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