Related objects

Learn more about

Show commands for: Magma / SageMath

Decomposition of \( S_{12}^{\mathrm{new}}(14) \) into irreducible Hecke orbits

magma: S := CuspForms(14,12);
magma: N := Newforms(S);
sage: N = Newforms(14,12,names="a")
Label Dimension Field $q$-expansion of eigenform
14.12.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(32q^{2} \) \(\mathstrut-\) \(396q^{3} \) \(\mathstrut+\) \(1024q^{4} \) \(\mathstrut+\) \(7350q^{5} \) \(\mathstrut+\) \(12672q^{6} \) \(\mathstrut+\) \(16807q^{7} \) \(\mathstrut-\) \(32768q^{8} \) \(\mathstrut-\) \(20331q^{9} \) \(\mathstrut+O(q^{10}) \)
14.12.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(32q^{2} \) \(\mathstrut-\) \(90q^{3} \) \(\mathstrut+\) \(1024q^{4} \) \(\mathstrut-\) \(7480q^{5} \) \(\mathstrut-\) \(2880q^{6} \) \(\mathstrut-\) \(16807q^{7} \) \(\mathstrut+\) \(32768q^{8} \) \(\mathstrut-\) \(169047q^{9} \) \(\mathstrut+O(q^{10}) \)
14.12.1.c 2 $\Q(\alpha_{ 3 })$ \(q \) \(\mathstrut-\) \(32q^{2} \) \(\mathstrut+\) \(\bigl(- \alpha_{3} \) \(\mathstrut- 32\bigr)q^{3} \) \(\mathstrut+\) \(1024q^{4} \) \(\mathstrut+\) \(\bigl(- 21 \alpha_{3} \) \(\mathstrut- 4214\bigr)q^{5} \) \(\mathstrut+\) \(\bigl(32 \alpha_{3} \) \(\mathstrut+ 1024\bigr)q^{6} \) \(\mathstrut-\) \(16807q^{7} \) \(\mathstrut-\) \(32768q^{8} \) \(\mathstrut+\) \(\bigl(- 350 \alpha_{3} \) \(\mathstrut- 65803\bigr)q^{9} \) \(\mathstrut+O(q^{10}) \)
14.12.1.d 2 $\Q(\alpha_{ 4 })$ \(q \) \(\mathstrut+\) \(32q^{2} \) \(\mathstrut+\) \(\bigl(\alpha_{4} \) \(\mathstrut- 32\bigr)q^{3} \) \(\mathstrut+\) \(1024q^{4} \) \(\mathstrut+\) \(\bigl(3 \alpha_{4} \) \(\mathstrut+ 2298\bigr)q^{5} \) \(\mathstrut+\) \(\bigl(32 \alpha_{4} \) \(\mathstrut- 1024\bigr)q^{6} \) \(\mathstrut+\) \(16807q^{7} \) \(\mathstrut+\) \(32768q^{8} \) \(\mathstrut+\) \(\bigl(- 350 \alpha_{4} \) \(\mathstrut+ 156397\bigr)q^{9} \) \(\mathstrut+O(q^{10}) \)

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 3 })$ \(x ^{2} \) \(\mathstrut +\mathstrut 414 x \) \(\mathstrut -\mathstrut 110320\)
$\Q(\alpha_{ 4 })$ \(x ^{2} \) \(\mathstrut +\mathstrut 286 x \) \(\mathstrut -\mathstrut 332520\)

Decomposition of \( S_{12}^{\mathrm{old}}(14) \) into lower level spaces

\( S_{12}^{\mathrm{old}}(14) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/7/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(7)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/1/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(1)) }^{\oplus 4 } $