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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 (8 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	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1058.4.a.a	$1058$	$4$	1058.a	1.a	$1$	$1$	$1$	$62.424$	\(\Q\)	None	✓				46.4.a.a	$1$	$1$	\(-2\)	\(-1\)	\(10\)	\(12\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+4q^{4}+10q^{5}+2q^{6}+\cdots\)
1058.4.a.e	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	\(\Q(\sqrt{3}) \)	None	✓	✓			1058.4.a.e	$2$	$1$	\(-4\)	\(-10\)	\(0\)	\(0\)		$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-2q^{2}-5q^{3}+4q^{4}-\beta q^{5}+10q^{6}+\cdots\)
1058.4.a.f	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	\(\Q(\sqrt{41}) \)	None	✓				46.4.a.c	$1$	$1$	\(-4\)	\(-1\)	\(-10\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1-3\beta )q^{3}+4q^{4}+(-4-2\beta )q^{5}+\cdots\)
1058.4.a.g	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	\(\Q(\sqrt{3}) \)	None	✓	✓			1058.4.a.g	$1$	$1$	\(-4\)	\(2\)	\(-12\)	\(18\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1+3\beta )q^{3}+4q^{4}+(-6-\beta )q^{5}+\cdots\)
1058.4.a.h	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	\(\Q(\sqrt{3}) \)	None	✓	✓			1058.4.a.g	$1$	$1$	\(-4\)	\(2\)	\(12\)	\(-18\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1+3\beta )q^{3}+4q^{4}+(6+\beta )q^{5}+\cdots\)
1058.4.a.k	$1058$	$4$	1058.a	1.a	$1$	$3$	$3$	$62.424$	3.3.6584.1	None	✓	✓			1058.4.a.k	$1$	$1$	\(-6\)	\(-2\)	\(-9\)	\(30\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots\)
1058.4.a.l	$1058$	$4$	1058.a	1.a	$1$	$3$	$3$	$62.424$	3.3.6584.1	None	✓	✓			1058.4.a.k	$1$	$1$	\(-6\)	\(-2\)	\(9\)	\(-30\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots\)
1058.4.a.t	$1058$	$4$	1058.a	1.a	$1$	$15$	$15$	$62.424$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		46.4.c.b	$1$	$1$	\(-30\)	\(1\)	\(0\)	\(-80\)		$+$	$-$	$-$	$23^{4}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{4}q^{3}+4q^{4}-\beta _{7}q^{5}-2\beta _{4}q^{6}+\cdots\)

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