LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twist	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 148 matches)

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Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
1650.2.a.a	$1$	$13.175$	$\Q$	None	$-1$	$-1$	$0$	$-3$	$+$	$q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots$
1650.2.a.b	$1$	$13.175$	$\Q$	None	$-1$	$-1$	$0$	$0$	$+$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
1650.2.a.c	$1$	$13.175$	$\Q$	None	$-1$	$-1$	$0$	$2$	$-$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
1650.2.a.d	$1$	$13.175$	$\Q$	None	$-1$	$-1$	$0$	$2$	$+$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
1650.2.a.e	$1$	$13.175$	$\Q$	None	$-1$	$1$	$0$	$-4$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots$
1650.2.a.f	$1$	$13.175$	$\Q$	None	$-1$	$1$	$0$	$-3$	$+$	$q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots$
1650.2.a.g	$1$	$13.175$	$\Q$	None	$-1$	$1$	$0$	$-1$	$+$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
1650.2.a.h	$1$	$13.175$	$\Q$	None	$-1$	$1$	$0$	$0$	$+$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
1650.2.a.i	$1$	$13.175$	$\Q$	None	$-1$	$1$	$0$	$2$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
1650.2.a.j	$1$	$13.175$	$\Q$	None	$-1$	$1$	$0$	$2$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
1650.2.a.k	$1$	$13.175$	$\Q$	None	$-1$	$1$	$0$	$4$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots$
1650.2.a.l	$1$	$13.175$	$\Q$	None	$1$	$-1$	$0$	$-2$	$+$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$
1650.2.a.m	$1$	$13.175$	$\Q$	None	$1$	$-1$	$0$	$-2$	$-$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$
1650.2.a.n	$1$	$13.175$	$\Q$	None	$1$	$-1$	$0$	$-2$	$+$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$
1650.2.a.o	$1$	$13.175$	$\Q$	None	$1$	$-1$	$0$	$1$	$-$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
1650.2.a.p	$1$	$13.175$	$\Q$	None	$1$	$-1$	$0$	$3$	$-$	$q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots$
1650.2.a.q	$1$	$13.175$	$\Q$	None	$1$	$1$	$0$	$-2$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
1650.2.a.r	$1$	$13.175$	$\Q$	None	$1$	$1$	$0$	$0$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
1650.2.a.s	$1$	$13.175$	$\Q$	None	$1$	$1$	$0$	$3$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
1650.2.a.t	$1$	$13.175$	$\Q$	None	$1$	$1$	$0$	$4$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
1650.2.a.u	$2$	$13.175$	$\Q(\sqrt{2}) $	None	$-2$	$-2$	$0$	$-4$	$-$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots$
1650.2.a.v	$2$	$13.175$	$\Q(\sqrt{73}) $	None	$-2$	$-2$	$0$	$1$	$+$	$q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots$
1650.2.a.w	$2$	$13.175$	$\Q(\sqrt{10}) $	None	$-2$	$2$	$0$	$4$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots$
1650.2.a.x	$2$	$13.175$	$\Q(\sqrt{10}) $	None	$2$	$-2$	$0$	$-4$	$-$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots$
1650.2.a.y	$2$	$13.175$	$\Q(\sqrt{73}) $	None	$2$	$2$	$0$	$-1$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}-\beta q^{7}+q^{8}+\cdots$
1650.2.a.z	$2$	$13.175$	$\Q(\sqrt{2}) $	None	$2$	$2$	$0$	$4$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots$
1650.2.c.a	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$
1650.2.c.b	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots$
1650.2.c.c	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$
1650.2.c.d	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$
1650.2.c.e	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$
1650.2.c.f	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots$
1650.2.c.g	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots$
1650.2.c.h	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$
1650.2.c.i	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots$
1650.2.c.j	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots$
1650.2.c.k	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots$
1650.2.c.l	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots$
1650.2.c.m	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$
1650.2.c.n	$2$	$13.175$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$
1650.2.c.o	$4$	$13.175$	$\Q(i, \sqrt{73})$	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots$
1650.2.d.a	$2$	$13.175$	$\Q(\sqrt{-2}) $	None	$-2$	$2$	$0$	$0$		$q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
1650.2.d.b	$2$	$13.175$	$\Q(\sqrt{-2}) $	None	$2$	$2$	$0$	$0$		$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
1650.2.d.c	$8$	$13.175$	8.0.2051727616.3	None	$-8$	$-2$	$0$	$0$		$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
1650.2.d.d	$8$	$13.175$	8.0.$\cdots$.1	None	$-8$	$-1$	$0$	$0$		$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots$
1650.2.d.e	$8$	$13.175$	8.0.$\cdots$.1	None	$-8$	$1$	$0$	$0$		$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots$
1650.2.d.f	$8$	$13.175$	8.0.2051727616.3	None	$8$	$-2$	$0$	$0$		$q+q^{2}+(-\beta _{3}-\beta _{4})q^{3}+q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$
1650.2.d.g	$8$	$13.175$	8.0.$\cdots$.1	None	$8$	$-1$	$0$	$0$		$q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots$
1650.2.d.h	$8$	$13.175$	8.0.$\cdots$.1	None	$8$	$1$	$0$	$0$		$q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots$
1650.2.d.i	$12$	$13.175$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$-12$	$0$	$0$	$0$		$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots$

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Degree 1	Degree 2
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$\zeta$ zeros

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
1650.2.a.a	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(-1\)	\(0\)	\(-3\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
1650.2.a.b	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
1650.2.a.c	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(-1\)	\(0\)	\(2\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.d	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(-1\)	\(0\)	\(2\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.e	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(-4\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
1650.2.a.f	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(-3\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
1650.2.a.g	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(-1\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1650.2.a.h	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(0\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1650.2.a.i	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(2\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.j	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(2\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.k	\(1\)	\(13.175\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(4\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
1650.2.a.l	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(-2\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.m	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(-2\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.n	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(-2\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.o	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(1\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
1650.2.a.p	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(3\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
1650.2.a.q	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(-2\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.r	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(0\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
1650.2.a.s	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(3\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
1650.2.a.t	\(1\)	\(13.175\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(4\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
1650.2.a.u	\(2\)	\(13.175\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(-2\)	\(0\)	\(-4\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1650.2.a.v	\(2\)	\(13.175\)	\(\Q(\sqrt{73}) \)	None	\(-2\)	\(-2\)	\(0\)	\(1\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
1650.2.a.w	\(2\)	\(13.175\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(2\)	\(0\)	\(4\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots\)
1650.2.a.x	\(2\)	\(13.175\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(-2\)	\(0\)	\(-4\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots\)
1650.2.a.y	\(2\)	\(13.175\)	\(\Q(\sqrt{73}) \)	None	\(2\)	\(2\)	\(0\)	\(-1\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}-\beta q^{7}+q^{8}+\cdots\)
1650.2.a.z	\(2\)	\(13.175\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(2\)	\(0\)	\(4\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots\)
1650.2.c.a	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1650.2.c.b	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
1650.2.c.c	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.d	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.e	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1650.2.c.f	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
1650.2.c.g	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
1650.2.c.h	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.i	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
1650.2.c.j	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1650.2.c.k	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
1650.2.c.l	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
1650.2.c.m	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1650.2.c.n	\(2\)	\(13.175\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1650.2.c.o	\(4\)	\(13.175\)	\(\Q(i, \sqrt{73})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)
1650.2.d.a	\(2\)	\(13.175\)	\(\Q(\sqrt{-2}) \)	None	\(-2\)	\(2\)	\(0\)	\(0\)		\(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1650.2.d.b	\(2\)	\(13.175\)	\(\Q(\sqrt{-2}) \)	None	\(2\)	\(2\)	\(0\)	\(0\)		\(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1650.2.d.c	\(8\)	\(13.175\)	8.0.2051727616.3	None	\(-8\)	\(-2\)	\(0\)	\(0\)		\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1650.2.d.d	\(8\)	\(13.175\)	8.0.\(\cdots\).1	None	\(-8\)	\(-1\)	\(0\)	\(0\)		\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.e	\(8\)	\(13.175\)	8.0.\(\cdots\).1	None	\(-8\)	\(1\)	\(0\)	\(0\)		\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.f	\(8\)	\(13.175\)	8.0.2051727616.3	None	\(8\)	\(-2\)	\(0\)	\(0\)		\(q+q^{2}+(-\beta _{3}-\beta _{4})q^{3}+q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
1650.2.d.g	\(8\)	\(13.175\)	8.0.\(\cdots\).1	None	\(8\)	\(-1\)	\(0\)	\(0\)		\(q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.h	\(8\)	\(13.175\)	8.0.\(\cdots\).1	None	\(8\)	\(1\)	\(0\)	\(0\)		\(q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.i	\(12\)	\(13.175\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(-12\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots\)

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L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.