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Decomposition of \( S_{10}^{\mathrm{new}}(2) \) into irreducible Hecke orbits

magma: S := CuspForms(2,10);
magma: N := Newforms(S);
sage: N = Newforms(2,10,names="a")
Label Dimension Field $q$-expansion of eigenform
2.10.1.a 1 \(\Q\) \(q \) \(\mathstrut+\) \(16q^{2} \) \(\mathstrut-\) \(156q^{3} \) \(\mathstrut+\) \(256q^{4} \) \(\mathstrut+\) \(870q^{5} \) \(\mathstrut-\) \(2496q^{6} \) \(\mathstrut-\) \(952q^{7} \) \(\mathstrut+\) \(4096q^{8} \) \(\mathstrut+\) \(4653q^{9} \) \(\mathstrut+O(q^{10}) \)