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Decomposition of \( S_{10}^{\mathrm{new}}(14) \) into irreducible Hecke orbits

magma: S := CuspForms(14,10);
magma: N := Newforms(S);
sage: N = Newforms(14,10,names="a")
Label Dimension Field $q$-expansion of eigenform
14.10.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(16q^{2} \) \(\mathstrut-\) \(6q^{3} \) \(\mathstrut+\) \(256q^{4} \) \(\mathstrut+\) \(560q^{5} \) \(\mathstrut+\) \(96q^{6} \) \(\mathstrut-\) \(2401q^{7} \) \(\mathstrut-\) \(4096q^{8} \) \(\mathstrut-\) \(19647q^{9} \) \(\mathstrut+O(q^{10}) \)
14.10.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(16q^{2} \) \(\mathstrut+\) \(170q^{3} \) \(\mathstrut+\) \(256q^{4} \) \(\mathstrut+\) \(544q^{5} \) \(\mathstrut+\) \(2720q^{6} \) \(\mathstrut-\) \(2401q^{7} \) \(\mathstrut+\) \(4096q^{8} \) \(\mathstrut+\) \(9217q^{9} \) \(\mathstrut+O(q^{10}) \)
14.10.1.c 2 $\Q(\alpha_{ 3 })$ \(q \) \(\mathstrut-\) \(16q^{2} \) \(\mathstrut+\) \(\bigl(\alpha_{3} \) \(\mathstrut+ 16\bigr)q^{3} \) \(\mathstrut+\) \(256q^{4} \) \(\mathstrut+\) \(\bigl(\frac{21}{5} \alpha_{3} \) \(\mathstrut- \frac{6342}{5}\bigr)q^{5} \) \(\mathstrut+\) \(\bigl(- 16 \alpha_{3} \) \(\mathstrut- 256\bigr)q^{6} \) \(\mathstrut+\) \(2401q^{7} \) \(\mathstrut-\) \(4096q^{8} \) \(\mathstrut+\) \(\bigl(- 14 \alpha_{3} \) \(\mathstrut+ 37669\bigr)q^{9} \) \(\mathstrut+O(q^{10}) \)

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 3 })\cong$ \(\Q(\sqrt{2305}) \) \(x ^{2} \) \(\mathstrut +\mathstrut 46 x \) \(\mathstrut -\mathstrut 57096\)

Decomposition of \( S_{10}^{\mathrm{old}}(14) \) into lower level spaces

\( S_{10}^{\mathrm{old}}(14) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/7/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(7)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(2)) }^{\oplus 2 } $