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Decomposition of \( S_{12}^{\mathrm{new}}(6) \) into irreducible Hecke orbits

magma: S := CuspForms(6,12);
magma: N := Newforms(S);
sage: N = Newforms(6,12,names="a")
Label Dimension Field $q$-expansion of eigenform
6.12.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(32q^{2} \) \(\mathstrut-\) \(243q^{3} \) \(\mathstrut+\) \(1024q^{4} \) \(\mathstrut+\) \(5766q^{5} \) \(\mathstrut+\) \(7776q^{6} \) \(\mathstrut+\) \(72464q^{7} \) \(\mathstrut-\) \(32768q^{8} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)
6.12.1.b 1 \(\Q\) \(q \) \(\mathstrut-\) \(32q^{2} \) \(\mathstrut+\) \(243q^{3} \) \(\mathstrut+\) \(1024q^{4} \) \(\mathstrut-\) \(11730q^{5} \) \(\mathstrut-\) \(7776q^{6} \) \(\mathstrut-\) \(50008q^{7} \) \(\mathstrut-\) \(32768q^{8} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)
6.12.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(32q^{2} \) \(\mathstrut+\) \(243q^{3} \) \(\mathstrut+\) \(1024q^{4} \) \(\mathstrut+\) \(3630q^{5} \) \(\mathstrut+\) \(7776q^{6} \) \(\mathstrut+\) \(32936q^{7} \) \(\mathstrut+\) \(32768q^{8} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{12}^{\mathrm{old}}(6) \) into lower level spaces

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