# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{12}^{\mathrm{new}}(24)$ into irreducible Hecke orbits

magma: S := CuspForms(24,12);
magma: N := Newforms(S);
sage: N = Newforms(24,12,names="a")
Label Dimension Field $q$-expansion of eigenform
24.12.1.a 1 $\Q$ $q$ $\mathstrut-$ $243q^{3}$ $\mathstrut-$ $7130q^{5}$ $\mathstrut-$ $19536q^{7}$ $\mathstrut+$ $59049q^{9}$ $\mathstrut+O(q^{10})$
24.12.1.b 1 $\Q$ $q$ $\mathstrut-$ $243q^{3}$ $\mathstrut+$ $1190q^{5}$ $\mathstrut+$ $18480q^{7}$ $\mathstrut+$ $59049q^{9}$ $\mathstrut+O(q^{10})$
24.12.1.c 1 $\Q$ $q$ $\mathstrut+$ $243q^{3}$ $\mathstrut+$ $1870q^{5}$ $\mathstrut-$ $72312q^{7}$ $\mathstrut+$ $59049q^{9}$ $\mathstrut+O(q^{10})$
24.12.1.d 2 $\Q(\alpha_{ 4 })$ $q$ $\mathstrut+$ $243q^{3}$ $\mathstrut+$ $\bigl(\frac{1}{2} \alpha_{4}$ $\mathstrut+ 243\bigr)q^{5}$ $\mathstrut+$ $\bigl(- \frac{1}{2} \alpha_{4}$ $\mathstrut+ 19427\bigr)q^{7}$ $\mathstrut+$ $59049q^{9}$ $\mathstrut+O(q^{10})$

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 4 })\cong$ $\Q(\sqrt{3061})$ $x ^{2}$ $\mathstrut -\mathstrut 2156 x$ $\mathstrut -\mathstrut 450200732$

## Decomposition of $S_{12}^{\mathrm{old}}(24)$ into lower level spaces

$S_{12}^{\mathrm{old}}(24)$ $\cong$ $\href{ /ModularForm/GL2/Q/holomorphic/12/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(12)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/8/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(8)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(6)) }^{\oplus 3 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/4/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(4)) }^{\oplus 4 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(3)) }^{\oplus 4 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/1/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(1)) }^{\oplus 8 }$