Related objects

Learn more about

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 } $