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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.b	$300$	$8$	300.a	1.a	$1$	$1$	$1$	$93.716$	\(\Q\)	None	✓				60.8.d.a	$1$	$0$	\(0\)	\(-27\)	\(0\)	\(-722\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}-722q^{7}+3^{6}q^{9}-3994q^{11}+\cdots\)
300.8.a.e	$300$	$8$	300.a	1.a	$1$	$1$	$1$	$93.716$	\(\Q\)	None	✓				60.8.a.a	$1$	$0$	\(0\)	\(27\)	\(0\)	\(-1028\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}-1028q^{7}+3^{6}q^{9}+3096q^{11}+\cdots\)
300.8.a.g	$300$	$8$	300.a	1.a	$1$	$1$	$1$	$93.716$	\(\Q\)	None	✓				12.8.a.a	$1$	$0$	\(0\)	\(27\)	\(0\)	\(832\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+832q^{7}+3^{6}q^{9}-2484q^{11}+\cdots\)
300.8.a.h	$300$	$8$	300.a	1.a	$1$	$1$	$1$	$93.716$	\(\Q\)	None	✓				60.8.a.b	$1$	$0$	\(0\)	\(27\)	\(0\)	\(832\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+832q^{7}+3^{6}q^{9}+3156q^{11}+\cdots\)
300.8.a.j	$300$	$8$	300.a	1.a	$1$	$2$	$2$	$93.716$	\(\Q(\sqrt{1129}) \)	None	✓				60.8.d.b	$1$	$0$	\(0\)	\(-54\)	\(0\)	\(906\)		$-$	$+$	$-$	$+$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}+(453-\beta )q^{7}+3^{6}q^{9}+(3171+\cdots)q^{11}+\cdots\)
300.8.a.m	$300$	$8$	300.a	1.a	$1$	$3$	$3$	$93.716$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓		300.8.a.m	$1$	$0$	\(0\)	\(-81\)	\(0\)	\(-351\)		$-$	$+$	$-$	$+$	$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}+(-117-\beta _{1})q^{7}+3^{6}q^{9}+\cdots\)
300.8.a.n	$300$	$8$	300.a	1.a	$1$	$3$	$3$	$93.716$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓		300.8.a.m	$1$	$0$	\(0\)	\(81\)	\(0\)	\(351\)		$-$	$-$	$+$	$+$	$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+(117+\beta _{1})q^{7}+3^{6}q^{9}+(1046+\cdots)q^{11}+\cdots\)

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