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Properties

Label 430.2.p
Level $430$
Weight $2$
Character orbit 430.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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
430.2.p.a 430.p 215.p $132$ $3.434$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{14}]$

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

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