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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	3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
300.8.a.a	$300$	$8$	300.a	1.a	$1$	$1$	$1$	$93.716$	\(\Q\)	None	✓				12.8.a.b	$1$	$1$	\(0\)	\(-27\)	\(0\)	\(-1112\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}-1112q^{7}+3^{6}q^{9}-5724q^{11}+\cdots\)
300.8.a.c	$300$	$8$	300.a	1.a	$1$	$1$	$1$	$93.716$	\(\Q\)	None	✓				60.8.a.c	$1$	$1$	\(0\)	\(-27\)	\(0\)	\(-92\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}-92q^{7}+3^{6}q^{9}+3456q^{11}+\cdots\)
300.8.a.d	$300$	$8$	300.a	1.a	$1$	$1$	$1$	$93.716$	\(\Q\)	None	✓				60.8.a.d	$1$	$1$	\(0\)	\(-27\)	\(0\)	\(1408\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}+1408q^{7}+3^{6}q^{9}-4044q^{11}+\cdots\)
300.8.a.f	$300$	$8$	300.a	1.a	$1$	$1$	$1$	$93.716$	\(\Q\)	None	✓				60.8.d.a	$1$	$1$	\(0\)	\(27\)	\(0\)	\(722\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+722q^{7}+3^{6}q^{9}-3994q^{11}+\cdots\)
300.8.a.i	$300$	$8$	300.a	1.a	$1$	$2$	$2$	$93.716$	\(\Q(\sqrt{319}) \)	None	✓	✓	✓		300.8.a.i	$1$	$1$	\(0\)	\(-54\)	\(0\)	\(-154\)		$-$	$+$	$+$	$-$	$2^{2}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}+(-77+\beta )q^{7}+3^{6}q^{9}+(-714+\cdots)q^{11}+\cdots\)
300.8.a.k	$300$	$8$	300.a	1.a	$1$	$2$	$2$	$93.716$	\(\Q(\sqrt{1129}) \)	None	✓				60.8.d.b	$1$	$1$	\(0\)	\(54\)	\(0\)	\(-906\)		$-$	$-$	$-$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+(-453-\beta )q^{7}+3^{6}q^{9}+\cdots\)
300.8.a.l	$300$	$8$	300.a	1.a	$1$	$2$	$2$	$93.716$	\(\Q(\sqrt{319}) \)	None	✓	✓			300.8.a.i	$1$	$1$	\(0\)	\(54\)	\(0\)	\(154\)		$-$	$-$	$-$	$-$	$2^{2}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+(77+\beta )q^{7}+3^{6}q^{9}+(-714+\cdots)q^{11}+\cdots\)

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