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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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Results (4 matches)

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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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1232.4.a.e	$1232$	$4$	1232.a	1.a	$1$	$1$	$1$	$72.690$	\(\Q\)	None	✓				154.4.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+7q^{7}-3^{3}q^{9}-11q^{11}+26q^{13}+\cdots\)
1232.4.a.q	$1232$	$4$	1232.a	1.a	$1$	$3$	$3$	$72.690$	3.3.7636.1	None	✓				154.4.a.i	$1$	$0$	\(0\)	\(-6\)	\(26\)	\(21\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(9-\beta _{2})q^{5}+7q^{7}+\cdots\)
1232.4.a.v	$1232$	$4$	1232.a	1.a	$1$	$4$	$4$	$72.690$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				308.4.a.d	$1$	$0$	\(0\)	\(3\)	\(1\)	\(28\)		$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}+7q^{7}+(-5+\cdots)q^{9}+\cdots\)
1232.4.a.w	$1232$	$4$	1232.a	1.a	$1$	$4$	$4$	$72.690$	4.4.509800.1	None	✓				77.4.a.c	$1$	$0$	\(0\)	\(12\)	\(-18\)	\(28\)		$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{2})q^{3}+(-5+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)

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