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Decomposition of \( S_{12}^{\mathrm{new}}(3) \) into irreducible Hecke orbits

magma: S := CuspForms(3,12);
magma: N := Newforms(S);
sage: N = Newforms(3,12,names="a")
Label Dimension Field $q$-expansion of eigenform
3.12.1.a 1 \(\Q\) \(q \) \(\mathstrut+\) \(78q^{2} \) \(\mathstrut-\) \(243q^{3} \) \(\mathstrut+\) \(4036q^{4} \) \(\mathstrut-\) \(5370q^{5} \) \(\mathstrut-\) \(18954q^{6} \) \(\mathstrut-\) \(27760q^{7} \) \(\mathstrut+\) \(155064q^{8} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{12}^{\mathrm{old}}(3) \) into lower level spaces

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