# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{12}^{\mathrm{new}}(23)$ into irreducible Hecke orbits

magma: S := CuspForms(23,12);
magma: N := Newforms(S);
sage: N = Newforms(23,12,names="a")
Label Dimension Field $q$-expansion of eigenform
23.12.1.a 8 $\Q(\alpha_{ 1 })$ $q + \ldots^\ast$
23.12.1.b 11 $\Q(\alpha_{ 2 })$ $q + \ldots^\ast$

${}^\ast$: The Fourier coefficients of this newform are large. They are available for download.
Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 1 })$ $x ^{8}$ $\mathstrut +\mathstrut 32 x ^{7}$ $\mathstrut -\mathstrut 10240 x ^{6}$ $\mathstrut -\mathstrut 243056 x ^{5}$ $\mathstrut +\mathstrut 32897712 x ^{4}$ $\mathstrut +\mathstrut 475545152 x ^{3}$ $\mathstrut -\mathstrut 32355612672 x ^{2}$ $\mathstrut -\mathstrut 118888316928 x$ $\mathstrut +\mathstrut 6030172585984$
$\Q(\alpha_{ 2 })$ $x ^{11}$ $\mathstrut -\mathstrut 32 x ^{10}$ $\mathstrut -\mathstrut 16384 x ^{9}$ $\mathstrut +\mathstrut 453021 x ^{8}$ $\mathstrut +\mathstrut 91689644 x ^{7}$ $\mathstrut -\mathstrut 2171413128 x ^{6}$ $\mathstrut -\mathstrut 205410732416 x ^{5}$ $\mathstrut +\mathstrut 4226023192464 x ^{4}$ $\mathstrut +\mathstrut 148783481621696 x ^{3}$ $\mathstrut -\mathstrut 3199980978790400 x ^{2}$ $\mathstrut +\mathstrut 5191695182200832 x$ $\mathstrut +\mathstrut 60024577238663168$