# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{12}^{\mathrm{new}}(18)$ into irreducible Hecke orbits

magma: S := CuspForms(18,12);
magma: N := Newforms(S);
sage: N = Newforms(18,12,names="a")
Label Dimension Field $q$-expansion of eigenform
18.12.1.a 1 $\Q$ $q$ $\mathstrut-$ $32q^{2}$ $\mathstrut+$ $1024q^{4}$ $\mathstrut-$ $3630q^{5}$ $\mathstrut+$ $32936q^{7}$ $\mathstrut-$ $32768q^{8}$ $\mathstrut+O(q^{10})$
18.12.1.b 1 $\Q$ $q$ $\mathstrut-$ $32q^{2}$ $\mathstrut+$ $1024q^{4}$ $\mathstrut+$ $5280q^{5}$ $\mathstrut-$ $49036q^{7}$ $\mathstrut-$ $32768q^{8}$ $\mathstrut+O(q^{10})$
18.12.1.c 1 $\Q$ $q$ $\mathstrut+$ $32q^{2}$ $\mathstrut+$ $1024q^{4}$ $\mathstrut-$ $5766q^{5}$ $\mathstrut+$ $72464q^{7}$ $\mathstrut+$ $32768q^{8}$ $\mathstrut+O(q^{10})$
18.12.1.d 1 $\Q$ $q$ $\mathstrut+$ $32q^{2}$ $\mathstrut+$ $1024q^{4}$ $\mathstrut-$ $5280q^{5}$ $\mathstrut-$ $49036q^{7}$ $\mathstrut+$ $32768q^{8}$ $\mathstrut+O(q^{10})$
18.12.1.e 1 $\Q$ $q$ $\mathstrut+$ $32q^{2}$ $\mathstrut+$ $1024q^{4}$ $\mathstrut+$ $11730q^{5}$ $\mathstrut-$ $50008q^{7}$ $\mathstrut+$ $32768q^{8}$ $\mathstrut+O(q^{10})$

## Decomposition of $S_{12}^{\mathrm{old}}(18)$ into lower level spaces

$S_{12}^{\mathrm{old}}(18)$ $\cong$ $\href{ /ModularForm/GL2/Q/holomorphic/9/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(9)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(6)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(3)) }^{\oplus 4 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/1/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(1)) }^{\oplus 6 }$