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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 (11 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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8624.2.a.h	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				4312.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+4q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
8624.2.a.m	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				616.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}-q^{11}-q^{15}+2q^{17}+\cdots\)
8624.2.a.x	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	\(\Q\)	None	✓				4312.2.a.a	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}+q^{9}-q^{11}-2q^{13}+\cdots\)
8624.2.a.bi	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{17}) \)	None	✓				616.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}-q^{11}+\cdots\)
8624.2.a.cd	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	\(\Q(\sqrt{2}) \)	None	✓				616.2.q.b	$1$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+\beta q^{5}+2\beta q^{9}-q^{11}+\cdots\)
8624.2.a.cf	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	\(\Q(\zeta_{14})^+\)	None	✓				616.2.q.c	$1$	$0$	\(0\)	\(-5\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{3}+(-1+3\beta _{1}-2\beta _{2})q^{5}+\cdots\)
8624.2.a.cm	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.229.1	None	✓				616.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{9}-q^{11}+\cdots\)
8624.2.a.ct	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	4.4.9248.1	None	✓				4312.2.a.ba	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{9}-q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
8624.2.a.cv	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	\(\Q(\sqrt{7}, \sqrt{15})\)	None	✓				4312.2.a.bb	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+\beta _{2}q^{5}+(2-\beta _{3})q^{9}-q^{11}+\cdots\)
8624.2.a.cy	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	4.4.11348.1	None	✓				616.2.a.h	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(2+\beta _{2}-\beta _{3})q^{9}+\cdots\)
8624.2.a.dd	$8624$	$2$	8624.a	1.a	$1$	$5$	$5$	$68.863$	5.5.352076.1	None	✓		✓		616.2.q.e	$1$	$0$	\(0\)	\(3\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{4})q^{5}+\cdots\)

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