Properties

Label 430.2.p
Level 430
Weight 2
Character orbit p
Rep. character \(\chi_{430}(59,\cdot)\)
Character field \(\Q(\zeta_{14})\)
Dimension 132
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.p (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(\zeta_{14})\)
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 420 132 288
Cusp forms 372 132 240
Eisenstein series 48 0 48

Trace form

\( 132q + 22q^{4} - 4q^{5} - 4q^{6} + 12q^{9} + O(q^{10}) \) \( 132q + 22q^{4} - 4q^{5} - 4q^{6} + 12q^{9} + 8q^{11} - 10q^{14} - 20q^{15} - 22q^{16} - 4q^{19} + 4q^{20} - 24q^{21} + 4q^{24} - 16q^{25} + 12q^{26} + 40q^{29} + 24q^{31} - 4q^{35} + 128q^{36} - 56q^{39} - 28q^{41} - 8q^{44} - 80q^{45} - 12q^{46} - 136q^{49} - 56q^{50} + 172q^{51} + 16q^{54} - 4q^{56} + 16q^{59} - 8q^{60} - 44q^{61} + 22q^{64} + 42q^{65} + 8q^{66} - 62q^{69} + 12q^{70} - 8q^{71} - 4q^{74} - 122q^{75} - 52q^{76} - 64q^{79} - 4q^{80} - 56q^{81} + 24q^{84} - 72q^{85} - 10q^{86} + 16q^{89} + 2q^{90} - 24q^{91} - 20q^{94} + 106q^{95} - 4q^{96} - 104q^{99} + O(q^{100}) \)

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.p.a \(132\) \(3.434\) 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