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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
115.4.a.a	$115$	$4$	115.a	1.a	$1$	$1$	$1$	$6.785$	\(\Q\)	None	✓	✓			115.4.a.a	$1$	$1$	\(1\)	\(4\)	\(-5\)	\(-32\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+4q^{3}-7q^{4}-5q^{5}+4q^{6}+\cdots\)
115.4.a.b	$115$	$4$	115.a	1.a	$1$	$1$	$1$	$6.785$	\(\Q\)	None	✓	✓			115.4.a.b	$1$	$1$	\(2\)	\(-3\)	\(5\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}-4q^{4}+5q^{5}-6q^{6}+\cdots\)
115.4.a.c	$115$	$4$	115.a	1.a	$1$	$2$	$2$	$6.785$	\(\Q(\sqrt{109}) \)	None	✓	✓	✓		115.4.a.c	$1$	$1$	\(-6\)	\(-3\)	\(10\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+(-1-\beta )q^{3}+q^{4}+5q^{5}+\cdots\)
115.4.a.d	$115$	$4$	115.a	1.a	$1$	$5$	$5$	$6.785$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓		115.4.a.d	$1$	$1$	\(-5\)	\(-6\)	\(-25\)	\(-15\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\cdots\)

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