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Properties

Label 430.2.x
Level $430$
Weight $2$
Character orbit 430.x
Rep. character $\chi_{430}(3,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $528$
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.x (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{84})\)
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 1680 528 1152
Cusp forms 1488 528 960
Eisenstein series 192 0 192

Trace form

\( 528 q - 4 q^{6} - 12 q^{7} + O(q^{10}) \) \( 528 q - 4 q^{6} - 12 q^{7} + 40 q^{13} + 88 q^{16} - 4 q^{17} + 16 q^{21} - 12 q^{23} + 8 q^{25} - 12 q^{28} + 36 q^{30} - 72 q^{31} - 124 q^{33} + 40 q^{35} - 268 q^{36} - 44 q^{38} + 56 q^{41} - 168 q^{43} - 24 q^{46} - 72 q^{47} - 24 q^{50} + 280 q^{51} + 16 q^{52} - 132 q^{53} - 24 q^{55} + 8 q^{56} - 20 q^{57} - 8 q^{60} - 72 q^{61} + 48 q^{62} - 84 q^{65} - 72 q^{66} - 40 q^{67} - 32 q^{68} - 24 q^{71} + 192 q^{73} + 48 q^{76} - 148 q^{77} - 40 q^{78} + 56 q^{82} - 28 q^{83} - 20 q^{86} - 216 q^{87} + 8 q^{90} - 48 q^{91} + 12 q^{92} + 108 q^{93} - 4 q^{95} + 4 q^{96} - 120 q^{97} + 96 q^{98} + O(q^{100}) \)

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.x.a 430.x 215.x $528$ $3.434$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{84}]$

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

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