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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
224.6.a.f	$224$	$6$	224.a	1.a	$1$	$3$	$3$	$35.926$	3.3.367637.1	None	✓	✓			224.6.a.e	$1$	$1$	\(0\)	\(8\)	\(-14\)	\(-147\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{3}+(-5-\beta _{2})q^{5}-7^{2}q^{7}+\cdots\)
224.6.a.g	$224$	$6$	224.a	1.a	$1$	$4$	$4$	$35.926$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓		224.6.a.g	$1$	$1$	\(0\)	\(-18\)	\(-30\)	\(-196\)		$+$	$+$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(-4-\beta _{1})q^{3}+(-7-\beta _{1}-\beta _{2})q^{5}+\cdots\)

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