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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1323.2.a.k	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				189.2.e.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+2q^{13}+4q^{16}-7q^{19}-5q^{25}+\cdots\)
1323.2.a.x	$1323$	$2$	1323.a	1.a	$1$	$3$	$3$	$10.564$	3.3.321.1	None	✓				189.2.e.e	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1323.2.a.bb	$1323$	$2$	1323.a	1.a	$1$	$4$	$4$	$10.564$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	✓			1323.2.a.bb	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2-\beta _{3})q^{5}+\cdots\)
1323.2.a.bc	$1323$	$2$	1323.a	1.a	$1$	$4$	$4$	$10.564$	4.4.7168.1	None	✓	✓			1323.2.a.bc	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+\beta _{3}q^{8}+\cdots\)

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