# 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

# Related objects

## 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

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