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Level	Weight	Analytic conductor	\(Nk^2\)	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
825.4.a.y	$825$	$4$	825.a	1.a	$1$	$5$	$5$	$48.677$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(-15\)	\(0\)	\(18\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(1+\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots\)
825.4.a.bb	$825$	$4$	825.a	1.a	$1$	$7$	$7$	$48.677$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(-21\)	\(0\)	\(-50\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots\)

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