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The results below are complete, since the LMFDB contains all newforms with trivial character and $Nk^2$ at most 40000

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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 (7 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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
392.6.a.b	$392$	$6$	392.a	1.a	$1$	$1$	$1$	$62.870$	\(\Q\)	None	✓				8.6.a.a	$1$	$1$	\(0\)	\(-20\)	\(74\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-20q^{3}+74q^{5}+157q^{9}+124q^{11}+\cdots\)
392.6.a.c	$392$	$6$	392.a	1.a	$1$	$1$	$1$	$62.870$	\(\Q\)	None	✓				56.6.a.a	$1$	$1$	\(0\)	\(6\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{3}-4q^{5}-207q^{9}-240q^{11}+\cdots\)
392.6.a.d	$392$	$6$	392.a	1.a	$1$	$2$	$2$	$62.870$	\(\Q(\sqrt{345}) \)	None	✓				56.6.a.e	$1$	$1$	\(0\)	\(6\)	\(-82\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(3+\beta )q^{3}+(-41+3\beta )q^{5}+(111+\cdots)q^{9}+\cdots\)
392.6.a.h	$392$	$6$	392.a	1.a	$1$	$4$	$4$	$62.870$	4.4.2732674592.1	None	✓	✓			392.6.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(209-\beta _{3})q^{9}+\cdots\)
392.6.a.i	$392$	$6$	392.a	1.a	$1$	$5$	$5$	$62.870$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		56.6.i.a	$1$	$1$	\(0\)	\(-13\)	\(-31\)	\(0\)		$-$	$-$	$+$	$2^{9}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{3}+(-6-\beta _{3})q^{5}+(47+\cdots)q^{9}+\cdots\)
392.6.a.k	$392$	$6$	392.a	1.a	$1$	$5$	$5$	$62.870$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				56.6.i.b	$1$	$1$	\(0\)	\(5\)	\(-81\)	\(0\)		$+$	$+$	$+$	$2^{9}\cdot 7$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-2^{4}-\beta _{1}-\beta _{2})q^{5}+\cdots\)
392.6.a.m	$392$	$6$	392.a	1.a	$1$	$6$	$6$	$62.870$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		392.6.a.m	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-20+\beta _{4}+\cdots)q^{9}+\cdots\)

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