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Note: Search results may be incomplete due to uncomputed quantities: atkin_lehner_string (110727 objects)

Level	Weight	Analytic conductor	\(Nk^2\)	Dim.
Bad \(p\)	Char.	Primitive character	Character order	Coefficient field
Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank
Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (3 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7
147.6.a.c	$147$	$6$	147.a	1.a	$1$	$1$	$1$	$23.576$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-9\)	\(11\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-9q^{3}-28q^{4}+11q^{5}+18q^{6}+\cdots\)
147.6.a.i	$147$	$6$	147.a	1.a	$1$	$2$	$2$	$23.576$	\(\Q(\sqrt{249}) \)	None	✓	$1$	$1$	\(-3\)	\(-18\)	\(-33\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-9q^{3}+(31+3\beta )q^{4}+\cdots\)
147.6.a.n	$147$	$6$	147.a	1.a	$1$	$6$	$6$	$23.576$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(2\)	\(-54\)	\(-100\)	\(0\)		$+$	$+$	$+$	$2^{4}\cdot 7^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-9q^{3}+(5^{2}-\beta _{1}+\beta _{4})q^{4}+\cdots\)