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Properties

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

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

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.j.a 430.j 215.i $44$ $3.434$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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