# Properties

 Label 96.2.c Level 96 Weight 2 Character orbit c Rep. character $$\chi_{96}(95,\cdot)$$ Character field $$\Q$$ Dimension 4 Newform subspaces 1 Sturm bound 32 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 96.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$12$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(96, [\chi])$$.

Total New Old
Modular forms 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

## Trace form

 $$4q + 4q^{9} + O(q^{10})$$ $$4q + 4q^{9} - 8q^{13} - 8q^{21} - 12q^{25} - 16q^{33} + 24q^{37} + 32q^{45} + 12q^{49} + 24q^{57} - 8q^{61} - 32q^{69} - 24q^{73} - 28q^{81} - 8q^{93} + 40q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
96.2.c.a $$4$$ $$0.767$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(96, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ $$1 - 2 T^{2} + 9 T^{4}$$
$5$ $$( 1 - 2 T^{2} + 25 T^{4} )^{2}$$
$7$ $$( 1 - 10 T^{2} + 49 T^{4} )^{2}$$
$11$ $$( 1 + 14 T^{2} + 121 T^{4} )^{2}$$
$13$ $$( 1 + 2 T + 13 T^{2} )^{4}$$
$17$ $$( 1 - 17 T^{2} )^{4}$$
$19$ $$( 1 - 2 T^{2} + 361 T^{4} )^{2}$$
$23$ $$( 1 + 14 T^{2} + 529 T^{4} )^{2}$$
$29$ $$( 1 - 50 T^{2} + 841 T^{4} )^{2}$$
$31$ $$( 1 - 58 T^{2} + 961 T^{4} )^{2}$$
$37$ $$( 1 - 6 T + 37 T^{2} )^{4}$$
$41$ $$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$
$43$ $$( 1 - 82 T^{2} + 1849 T^{4} )^{2}$$
$47$ $$( 1 - 34 T^{2} + 2209 T^{4} )^{2}$$
$53$ $$( 1 - 34 T^{2} + 2809 T^{4} )^{2}$$
$59$ $$( 1 + 110 T^{2} + 3481 T^{4} )^{2}$$
$61$ $$( 1 + 2 T + 61 T^{2} )^{4}$$
$67$ $$( 1 - 130 T^{2} + 4489 T^{4} )^{2}$$
$71$ $$( 1 + 110 T^{2} + 5041 T^{4} )^{2}$$
$73$ $$( 1 + 6 T + 73 T^{2} )^{4}$$
$79$ $$( 1 + 38 T^{2} + 6241 T^{4} )^{2}$$
$83$ $$( 1 + 158 T^{2} + 6889 T^{4} )^{2}$$
$89$ $$( 1 + 110 T^{2} + 7921 T^{4} )^{2}$$
$97$ $$( 1 - 10 T + 97 T^{2} )^{4}$$