LMFDB - Newforms of weight 12 for \(\Gamma

Show commands for: Magma / SageMath

Decomposition of $ S_{12}^{\mathrm{new}}(24) $ into irreducible Hecke orbits

magma: S := CuspForms(24,12);
magma: N := Newforms(S);

sage: N = Newforms(24,12,names="a")

Label	Dimension	Field	$q$-expansion of eigenform
24.12.1.a	1	$\Q$	$q $ $\mathstrut-$ $243q^{3} $ $\mathstrut-$ $7130q^{5} $ $\mathstrut-$ $19536q^{7} $ $\mathstrut+$ $59049q^{9} $ $\mathstrut+O(q^{10}) $
24.12.1.b	1	$\Q$	$q $ $\mathstrut-$ $243q^{3} $ $\mathstrut+$ $1190q^{5} $ $\mathstrut+$ $18480q^{7} $ $\mathstrut+$ $59049q^{9} $ $\mathstrut+O(q^{10}) $
24.12.1.c	1	$\Q$	$q $ $\mathstrut+$ $243q^{3} $ $\mathstrut+$ $1870q^{5} $ $\mathstrut-$ $72312q^{7} $ $\mathstrut+$ $59049q^{9} $ $\mathstrut+O(q^{10}) $
24.12.1.d	2	$\Q(\alpha_{ 4 })$	$q $ $\mathstrut+$ $243q^{3} $ $\mathstrut+$ $\bigl(\frac{1}{2} \alpha_{4} $ $\mathstrut+ 243\bigr)q^{5} $ $\mathstrut+$ $\bigl(- \frac{1}{2} \alpha_{4} $ $\mathstrut+ 19427\bigr)q^{7} $ $\mathstrut+$ $59049q^{9} $ $\mathstrut+O(q^{10}) $

The coefficient fields are:

Coefficient field	Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 4 })\cong$ $\Q(\sqrt{3061}) $	$x ^{2} $ $\mathstrut -\mathstrut 2156 x $ $\mathstrut -\mathstrut 450200732$

Decomposition of $ S_{12}^{\mathrm{old}}(24) $ into lower level spaces

$ S_{12}^{\mathrm{old}}(24) $ $\cong$ $ \href{ /ModularForm/GL2/Q/holomorphic/12/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(12)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/8/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(8)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(6)) }^{\oplus 3 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/4/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(4)) }^{\oplus 4 }\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 8 } $

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Decomposition of \( S_{12}^{\mathrm{new}}(24) \) into irreducible Hecke orbits

Decomposition of \( S_{12}^{\mathrm{old}}(24) \) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Dimension	Field	$q$-expansion of eigenform
24.12.1.a	1	\(\Q\)	\(q \) \(\mathstrut-\) \(243q^{3} \) \(\mathstrut-\) \(7130q^{5} \) \(\mathstrut-\) \(19536q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)
24.12.1.b	1	\(\Q\)	\(q \) \(\mathstrut-\) \(243q^{3} \) \(\mathstrut+\) \(1190q^{5} \) \(\mathstrut+\) \(18480q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)
24.12.1.c	1	\(\Q\)	\(q \) \(\mathstrut+\) \(243q^{3} \) \(\mathstrut+\) \(1870q^{5} \) \(\mathstrut-\) \(72312q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)
24.12.1.d	2	$\Q(\alpha_{ 4 })$	\(q \) \(\mathstrut+\) \(243q^{3} \) \(\mathstrut+\) \(\bigl(\frac{1}{2} \alpha_{4} \) \(\mathstrut+ 243\bigr)q^{5} \) \(\mathstrut+\) \(\bigl(- \frac{1}{2} \alpha_{4} \) \(\mathstrut+ 19427\bigr)q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)