LMFDB - Space of modular forms of level 980, weight 1, and Character 980.p

Defining parameters

The following table gives the dimensions of various subspaces of $M_{1}(980, [\chi])$.

The following table gives the dimensions of subspaces with specified projective image type.

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	12	0	0	0

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
980.1.p.a	$980$	$1$	980.p	140.p	$6$	$2$	$1$	$0.489$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-1$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
980.1.p.b	$980$	$1$	980.p	140.p	$6$	$2$	$1$	$0.489$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$1$	$1$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
980.1.p.c	$980$	$1$	980.p	140.p	$6$	$8$	$4$	$0.489$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots$

$ S_{1}^{\mathrm{old}}(980, [\chi]) \cong $ $S_{1}^{\mathrm{new}}(140, [\chi])$$^{\oplus 2}$

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