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The results below are complete, since the LMFDB contains all newforms with $Nk^2$ at most 4000

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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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
363.2.a.a	$363$	$2$	363.a	1.a	$1$	$1$	$1$	$2.899$	\(\Q\)	None	✓	✓			363.2.a.a	$1$	$0$	\(-2\)	\(-1\)	\(4\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
363.2.a.b	$363$	$2$	363.a	1.a	$1$	$1$	$1$	$2.899$	\(\Q\)	None	✓				33.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
363.2.a.c	$363$	$2$	363.a	1.a	$1$	$1$	$1$	$2.899$	\(\Q\)	None	✓	✓			363.2.a.a	$1$	$0$	\(2\)	\(-1\)	\(4\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots\)
363.2.a.i	$363$	$2$	363.a	1.a	$1$	$2$	$2$	$2.899$	\(\Q(\sqrt{5}) \)	None	✓		✓		33.2.e.b	$1$	$0$	\(3\)	\(-2\)	\(1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(1-\beta )q^{5}+\cdots\)

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