# Properties

 Label 96.2.f Level 96 Weight 2 Character orbit f Rep. character $$\chi_{96}(47,\cdot)$$ Character field $$\Q$$ Dimension 2 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.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$24$$ 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 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

## Trace form

 $$2q + 2q^{3} - 2q^{9} + O(q^{10})$$ $$2q + 2q^{3} - 2q^{9} - 4q^{19} - 10q^{25} - 10q^{27} + 8q^{33} + 20q^{43} + 14q^{49} + 16q^{51} - 4q^{57} - 28q^{67} + 4q^{73} - 10q^{75} - 14q^{81} - 20q^{97} + 16q^{99} + O(q^{100})$$

## 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.f.a $$2$$ $$0.767$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-2\beta q^{11}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(96, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 3}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ $$1 - 2 T + 3 T^{2}$$
$5$ $$( 1 + 5 T^{2} )^{2}$$
$7$ $$( 1 - 7 T^{2} )^{2}$$
$11$ $$( 1 - 6 T + 11 T^{2} )( 1 + 6 T + 11 T^{2} )$$
$13$ $$( 1 - 13 T^{2} )^{2}$$
$17$ $$( 1 - 6 T + 17 T^{2} )( 1 + 6 T + 17 T^{2} )$$
$19$ $$( 1 + 2 T + 19 T^{2} )^{2}$$
$23$ $$( 1 + 23 T^{2} )^{2}$$
$29$ $$( 1 + 29 T^{2} )^{2}$$
$31$ $$( 1 - 31 T^{2} )^{2}$$
$37$ $$( 1 - 37 T^{2} )^{2}$$
$41$ $$( 1 - 6 T + 41 T^{2} )( 1 + 6 T + 41 T^{2} )$$
$43$ $$( 1 - 10 T + 43 T^{2} )^{2}$$
$47$ $$( 1 + 47 T^{2} )^{2}$$
$53$ $$( 1 + 53 T^{2} )^{2}$$
$59$ $$( 1 - 6 T + 59 T^{2} )( 1 + 6 T + 59 T^{2} )$$
$61$ $$( 1 - 61 T^{2} )^{2}$$
$67$ $$( 1 + 14 T + 67 T^{2} )^{2}$$
$71$ $$( 1 + 71 T^{2} )^{2}$$
$73$ $$( 1 - 2 T + 73 T^{2} )^{2}$$
$79$ $$( 1 - 79 T^{2} )^{2}$$
$83$ $$( 1 - 18 T + 83 T^{2} )( 1 + 18 T + 83 T^{2} )$$
$89$ $$( 1 - 18 T + 89 T^{2} )( 1 + 18 T + 89 T^{2} )$$
$97$ $$( 1 + 10 T + 97 T^{2} )^{2}$$