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Decomposition of \( S_{10}^{\mathrm{new}}(24) \) into irreducible Hecke orbits

magma: S := CuspForms(24,10);
magma: N := Newforms(S);
sage: N = Newforms(24,10,names="a")
Label Dimension Field $q$-expansion of eigenform
24.10.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(81q^{3} \) \(\mathstrut+\) \(830q^{5} \) \(\mathstrut+\) \(672q^{7} \) \(\mathstrut+\) \(6561q^{9} \) \(\mathstrut+O(q^{10}) \)
24.10.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(81q^{3} \) \(\mathstrut-\) \(794q^{5} \) \(\mathstrut-\) \(5880q^{7} \) \(\mathstrut+\) \(6561q^{9} \) \(\mathstrut+O(q^{10}) \)
24.10.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(81q^{3} \) \(\mathstrut+\) \(614q^{5} \) \(\mathstrut+\) \(2184q^{7} \) \(\mathstrut+\) \(6561q^{9} \) \(\mathstrut+O(q^{10}) \)
24.10.1.d 2 $\Q(\alpha_{ 4 })$ \(q \) \(\mathstrut-\) \(81q^{3} \) \(\mathstrut+\) \(\bigl(\frac{1}{2} \alpha_{4} \) \(\mathstrut- 81\bigr)q^{5} \) \(\mathstrut+\) \(\bigl(- \frac{5}{2} \alpha_{4} \) \(\mathstrut- 2965\bigr)q^{7} \) \(\mathstrut+\) \(6561q^{9} \) \(\mathstrut+O(q^{10}) \)

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 4 })\cong$ \(\Q(\sqrt{109}) \) \(x ^{2} \) \(\mathstrut +\mathstrut 1220 x \) \(\mathstrut -\mathstrut 15700604\)

Decomposition of \( S_{10}^{\mathrm{old}}(24) \) into lower level spaces

\( S_{10}^{\mathrm{old}}(24) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/12/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(12)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/8/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(8)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(6)) }^{\oplus 3 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/4/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(4)) }^{\oplus 4 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(3)) }^{\oplus 4 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(2)) }^{\oplus 6 } $