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Decomposition of \( S_{6}^{\mathrm{new}}(14) \) into irreducible Hecke orbits

magma: S := CuspForms(14,6);
magma: N := Newforms(S);
sage: N = Newforms(14,6,names="a")
Label Dimension Field $q$-expansion of eigenform
14.6.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(4q^{2} \) \(\mathstrut+\) \(10q^{3} \) \(\mathstrut+\) \(16q^{4} \) \(\mathstrut+\) \(84q^{5} \) \(\mathstrut-\) \(40q^{6} \) \(\mathstrut+\) \(49q^{7} \) \(\mathstrut-\) \(64q^{8} \) \(\mathstrut-\) \(143q^{9} \) \(\mathstrut+O(q^{10}) \)
14.6.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(4q^{2} \) \(\mathstrut+\) \(8q^{3} \) \(\mathstrut+\) \(16q^{4} \) \(\mathstrut+\) \(10q^{5} \) \(\mathstrut+\) \(32q^{6} \) \(\mathstrut-\) \(49q^{7} \) \(\mathstrut+\) \(64q^{8} \) \(\mathstrut-\) \(179q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{6}^{\mathrm{old}}(14) \) into lower level spaces

\( S_{6}^{\mathrm{old}}(14) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/7/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(7)) }^{\oplus 2 } $