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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	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
322.4.a.c	$322$	$4$	322.a	1.a	$1$	$2$	$2$	$18.999$	\(\Q(\sqrt{57}) \)	None	✓	✓	✓	✓	322.4.a.c	$1$	$1$	\(4\)	\(1\)	\(-18\)	\(14\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta q^{3}+4q^{4}+(-8-2\beta )q^{5}+\cdots\)
322.4.a.e	$322$	$4$	322.a	1.a	$1$	$3$	$3$	$18.999$	3.3.3368.1	None	✓	✓	✓	✓	322.4.a.e	$1$	$1$	\(6\)	\(-7\)	\(-8\)	\(-21\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-2-\beta _{2})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots\)
322.4.a.f	$322$	$4$	322.a	1.a	$1$	$4$	$4$	$18.999$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	322.4.a.f	$1$	$1$	\(-8\)	\(-1\)	\(-2\)	\(28\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-\beta _{2}q^{5}+2\beta _{1}q^{6}+\cdots\)
322.4.a.g	$322$	$4$	322.a	1.a	$1$	$5$	$5$	$18.999$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	322.4.a.g	$1$	$1$	\(-10\)	\(-9\)	\(-2\)	\(-35\)		$+$	$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2+\beta _{4})q^{3}+4q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

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