Properties

Label 430.2.g
Level 430
Weight 2
Character orbit g
Rep. character \(\chi_{430}(257,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 44
Newform subspaces 2
Sturm bound 132
Trace bound 1

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Defining parameters

Level: \( N \) = \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 430.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

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

\( 44q + 8q^{6} + O(q^{10}) \) \( 44q + 8q^{6} - 16q^{13} - 44q^{16} + 8q^{17} + 16q^{21} + 24q^{23} + 8q^{25} + 64q^{31} - 32q^{35} + 52q^{36} - 40q^{38} - 40q^{41} - 28q^{43} - 48q^{47} + 16q^{52} - 80q^{53} + 8q^{56} + 40q^{57} + 16q^{60} - 32q^{66} + 16q^{67} + 8q^{68} + 56q^{78} - 76q^{81} + 72q^{83} - 20q^{86} + 4q^{87} - 4q^{90} - 24q^{92} - 28q^{95} - 8q^{96} - 24q^{97} + O(q^{100}) \)

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.g.a \(4\) \(3.434\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}-2\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
430.2.g.b \(40\) \(3.434\) None \(0\) \(0\) \(0\) \(0\)

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

$p$ $F_p(T)$
$2$ (\( 1 + T^{4} \))
$3$ (\( ( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} )( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} ) \))
$5$ (\( 1 + 8 T^{2} + 25 T^{4} \))
$7$ (\( 1 - 94 T^{4} + 2401 T^{8} \))
$11$ (\( ( 1 + 4 T + 11 T^{2} )^{4} \))
$13$ (\( ( 1 - 4 T + 8 T^{2} - 52 T^{3} + 169 T^{4} )^{2} \))
$17$ (\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 - 2 T + 17 T^{2} )^{2} \))
$19$ (\( ( 1 + 20 T^{2} + 361 T^{4} )^{2} \))
$23$ (\( ( 1 + 10 T + 50 T^{2} + 230 T^{3} + 529 T^{4} )^{2} \))
$29$ (\( ( 1 + 40 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 - 8 T + 31 T^{2} )^{4} \))
$37$ (\( 1 - 1294 T^{4} + 1874161 T^{8} \))
$41$ (\( ( 1 + 12 T + 41 T^{2} )^{4} \))
$43$ (\( 1 + 12 T + 72 T^{2} + 516 T^{3} + 1849 T^{4} \))
$47$ (\( ( 1 + 10 T + 50 T^{2} + 470 T^{3} + 2209 T^{4} )^{2} \))
$53$ (\( ( 1 + 2809 T^{4} )^{2} \))
$59$ (\( ( 1 - 59 T^{2} )^{4} \))
$61$ (\( ( 1 - 104 T^{2} + 3721 T^{4} )^{2} \))
$67$ (\( ( 1 + 4 T + 8 T^{2} + 268 T^{3} + 4489 T^{4} )^{2} \))
$71$ (\( ( 1 - 110 T^{2} + 5041 T^{4} )^{2} \))
$73$ (\( ( 1 - 24 T + 288 T^{2} - 1752 T^{3} + 5329 T^{4} )( 1 + 24 T + 288 T^{2} + 1752 T^{3} + 5329 T^{4} ) \))
$79$ (\( ( 1 - 58 T^{2} + 6241 T^{4} )^{2} \))
$83$ (\( ( 1 - 12 T + 72 T^{2} - 996 T^{3} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 - 22 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 - 18 T + 162 T^{2} - 1746 T^{3} + 9409 T^{4} )^{2} \))
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