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-twists	CM/RM discriminant	Inner twist count*	Is self-dual?	Analytic rank

Coefficient ring index	Coefficient ring gens.	Only for weight 1:	Projective image	Projective image type
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Results (displaying matches 1-50 of 281) Next

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
630.2.a.a	$1$	$5.031$	$\Q$	None	$-1$	$0$	$-1$	$-1$	$-$	$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
630.2.a.b	$1$	$5.031$	$\Q$	None	$-1$	$0$	$-1$	$1$	$+$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
630.2.a.c	$1$	$5.031$	$\Q$	None	$-1$	$0$	$-1$	$1$	$-$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
630.2.a.d	$1$	$5.031$	$\Q$	None	$-1$	$0$	$1$	$-1$	$+$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
630.2.a.e	$1$	$5.031$	$\Q$	None	$-1$	$0$	$1$	$-1$	$-$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
630.2.a.f	$1$	$5.031$	$\Q$	None	$-1$	$0$	$1$	$1$	$-$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
630.2.a.g	$1$	$5.031$	$\Q$	None	$1$	$0$	$-1$	$-1$	$-$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
630.2.a.h	$1$	$5.031$	$\Q$	None	$1$	$0$	$-1$	$1$	$-$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
630.2.a.i	$1$	$5.031$	$\Q$	None	$1$	$0$	$1$	$-1$	$-$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
630.2.a.j	$1$	$5.031$	$\Q$	None	$1$	$0$	$1$	$1$	$-$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
630.2.b.a	$8$	$5.031$	8.0.7442857984.4	None	$0$	$0$	$-8$	$-4$		$q+\beta _{3}q^{2}-q^{4}-q^{5}+\beta _{6}q^{7}-\beta _{3}q^{8}+\cdots$
630.2.b.b	$8$	$5.031$	8.0.7442857984.4	None	$0$	$0$	$8$	$-4$		$q-\beta _{3}q^{2}-q^{4}+q^{5}+\beta _{6}q^{7}+\beta _{3}q^{8}+\cdots$
630.2.d.a	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{-5})$	None	$-4$	$0$	$0$	$0$		$q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$
630.2.d.b	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{5})$	None	$-4$	$0$	$0$	$0$		$q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$
630.2.d.c	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{5})$	None	$4$	$0$	$0$	$0$		$q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
630.2.d.d	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{-5})$	None	$4$	$0$	$0$	$0$		$q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$
630.2.g.a	$2$	$5.031$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$0$		$q+iq^{2}-q^{4}+(-2-i)q^{5}+iq^{7}+\cdots$
630.2.g.b	$2$	$5.031$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$		$q+iq^{2}-q^{4}+(-1+2i)q^{5}-iq^{7}+\cdots$
630.2.g.c	$2$	$5.031$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$		$q+iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots$
630.2.g.d	$2$	$5.031$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$2$	$0$		$q+iq^{2}-q^{4}+(1+2i)q^{5}-iq^{7}-iq^{8}+\cdots$
630.2.g.e	$2$	$5.031$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$2$	$0$		$q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots$
630.2.g.f	$2$	$5.031$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$4$	$0$		$q+iq^{2}-q^{4}+(2-i)q^{5}-iq^{7}-iq^{8}+\cdots$
630.2.g.g	$4$	$5.031$	$\Q(i, \sqrt{6})$	None	$0$	$0$	$-4$	$0$		$q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$
630.2.i.a	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$-2$	$-3$	$-1$	$-1$		$q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
630.2.i.b	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$-2$	$-3$	$1$	$-4$		$q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots$
630.2.i.c	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$2$	$3$	$-1$	$-5$		$q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
630.2.i.d	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$2$	$3$	$1$	$-4$		$q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots$
630.2.i.e	$4$	$5.031$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$4$	$-6$	$2$	$-2$		$q+q^{2}+(-2-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
630.2.i.f	$12$	$5.031$	12.0.$\cdots$.1	None	$-12$	$2$	$-6$	$4$		$q-q^{2}+(\beta _{4}-\beta _{7})q^{3}+q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots$
630.2.i.g	$12$	$5.031$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$12$	$0$	$-6$	$4$		$q+q^{2}-\beta _{8}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots$
630.2.i.h	$12$	$5.031$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$12$	$2$	$6$	$8$		$q+q^{2}+(-\beta _{2}+\beta _{6})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
630.2.i.i	$16$	$5.031$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-16$	$2$	$8$	$4$		$q-q^{2}+(-\beta _{1}+\beta _{7})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots$
630.2.j.a	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$-1$	$-1$		$q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.b	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$1$	$-3$	$1$	$-1$		$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.c	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$1$	$-3$	$1$	$1$		$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.d	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$1$	$0$	$-1$	$-1$		$q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.e	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$1$	$3$	$1$	$-1$		$q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.f	$4$	$5.031$	$\Q(\zeta_{12})$	None	$2$	$0$	$-2$	$2$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots$
630.2.j.g	$4$	$5.031$	$\Q(\sqrt{-3}, \sqrt{-11})$	None	$2$	$1$	$2$	$2$		$q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots$
630.2.j.h	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	$2$	$2$	$-2$	$-2$		$q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
630.2.j.i	$6$	$5.031$	6.0.954288.1	None	$-3$	$-1$	$-3$	$3$		$q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
630.2.j.j	$6$	$5.031$	6.0.954288.1	None	$-3$	$-1$	$3$	$-3$		$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
630.2.j.k	$6$	$5.031$	6.0.954288.1	None	$-3$	$1$	$-3$	$-3$		$q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+\beta _{3}q^{4}+\beta _{3}q^{5}+\cdots$
630.2.j.l	$8$	$5.031$	8.0.856615824.2	None	$-4$	$-3$	$4$	$4$		$q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots$
630.2.k.a	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$-1$	$-4$		$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
630.2.k.b	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$-1$	$-1$		$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
630.2.k.c	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$-1$	$4$		$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
630.2.k.d	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$1$	$-4$		$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
630.2.k.e	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$1$	$0$	$-1$	$-4$		$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$
630.2.k.f	$2$	$5.031$	$\Q(\sqrt{-3}) $	None	$1$	$0$	$-1$	$1$		$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$

Introduction	Features
Universe	News

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
630.2.a.a	\(1\)	\(5.031\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(-1\)	\(-\)	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.b	\(1\)	\(5.031\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(1\)	\(+\)	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.c	\(1\)	\(5.031\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(1\)	\(-\)	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.d	\(1\)	\(5.031\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(-1\)	\(+\)	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.e	\(1\)	\(5.031\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(-1\)	\(-\)	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.f	\(1\)	\(5.031\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(1\)	\(-\)	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.g	\(1\)	\(5.031\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(-1\)	\(-\)	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
630.2.a.h	\(1\)	\(5.031\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(1\)	\(-\)	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
630.2.a.i	\(1\)	\(5.031\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-1\)	\(-\)	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
630.2.a.j	\(1\)	\(5.031\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(1\)	\(-\)	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
630.2.b.a	\(8\)	\(5.031\)	8.0.7442857984.4	None	\(0\)	\(0\)	\(-8\)	\(-4\)		\(q+\beta _{3}q^{2}-q^{4}-q^{5}+\beta _{6}q^{7}-\beta _{3}q^{8}+\cdots\)
630.2.b.b	\(8\)	\(5.031\)	8.0.7442857984.4	None	\(0\)	\(0\)	\(8\)	\(-4\)		\(q-\beta _{3}q^{2}-q^{4}+q^{5}+\beta _{6}q^{7}+\beta _{3}q^{8}+\cdots\)
630.2.d.a	\(4\)	\(5.031\)	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.d.b	\(4\)	\(5.031\)	\(\Q(\sqrt{-2}, \sqrt{5})\)	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.c	\(4\)	\(5.031\)	\(\Q(\sqrt{-2}, \sqrt{5})\)	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.d	\(4\)	\(5.031\)	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.g.a	\(2\)	\(5.031\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+iq^{2}-q^{4}+(-2-i)q^{5}+iq^{7}+\cdots\)
630.2.g.b	\(2\)	\(5.031\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+iq^{2}-q^{4}+(-1+2i)q^{5}-iq^{7}+\cdots\)
630.2.g.c	\(2\)	\(5.031\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
630.2.g.d	\(2\)	\(5.031\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+iq^{2}-q^{4}+(1+2i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.e	\(2\)	\(5.031\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
630.2.g.f	\(2\)	\(5.031\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+iq^{2}-q^{4}+(2-i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.g	\(4\)	\(5.031\)	\(\Q(i, \sqrt{6})\)	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
630.2.i.a	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(-3\)	\(-1\)	\(-1\)		\(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.b	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(-3\)	\(1\)	\(-4\)		\(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.c	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(3\)	\(-1\)	\(-5\)		\(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.d	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(3\)	\(1\)	\(-4\)		\(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.e	\(4\)	\(5.031\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(4\)	\(-6\)	\(2\)	\(-2\)		\(q+q^{2}+(-2-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
630.2.i.f	\(12\)	\(5.031\)	12.0.\(\cdots\).1	None	\(-12\)	\(2\)	\(-6\)	\(4\)		\(q-q^{2}+(\beta _{4}-\beta _{7})q^{3}+q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
630.2.i.g	\(12\)	\(5.031\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(12\)	\(0\)	\(-6\)	\(4\)		\(q+q^{2}-\beta _{8}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
630.2.i.h	\(12\)	\(5.031\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(12\)	\(2\)	\(6\)	\(8\)		\(q+q^{2}+(-\beta _{2}+\beta _{6})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
630.2.i.i	\(16\)	\(5.031\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-16\)	\(2\)	\(8\)	\(4\)		\(q-q^{2}+(-\beta _{1}+\beta _{7})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
630.2.j.a	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(-1\)	\(-1\)		\(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.b	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-3\)	\(1\)	\(-1\)		\(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.c	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-3\)	\(1\)	\(1\)		\(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.d	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(0\)	\(-1\)	\(-1\)		\(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.e	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(3\)	\(1\)	\(-1\)		\(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.f	\(4\)	\(5.031\)	\(\Q(\zeta_{12})\)	None	\(2\)	\(0\)	\(-2\)	\(2\)		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
630.2.j.g	\(4\)	\(5.031\)	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None	\(2\)	\(1\)	\(2\)	\(2\)		\(q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots\)
630.2.j.h	\(4\)	\(5.031\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	\(2\)	\(2\)	\(-2\)	\(-2\)		\(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
630.2.j.i	\(6\)	\(5.031\)	6.0.954288.1	None	\(-3\)	\(-1\)	\(-3\)	\(3\)		\(q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
630.2.j.j	\(6\)	\(5.031\)	6.0.954288.1	None	\(-3\)	\(-1\)	\(3\)	\(-3\)		\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
630.2.j.k	\(6\)	\(5.031\)	6.0.954288.1	None	\(-3\)	\(1\)	\(-3\)	\(-3\)		\(q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+\beta _{3}q^{4}+\beta _{3}q^{5}+\cdots\)
630.2.j.l	\(8\)	\(5.031\)	8.0.856615824.2	None	\(-4\)	\(-3\)	\(4\)	\(4\)		\(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots\)
630.2.k.a	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(-1\)	\(-4\)		\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
630.2.k.b	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(-1\)	\(-1\)		\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
630.2.k.c	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(-1\)	\(4\)		\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
630.2.k.d	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(1\)	\(-4\)		\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
630.2.k.e	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(0\)	\(-1\)	\(-4\)		\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
630.2.k.f	\(2\)	\(5.031\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(0\)	\(-1\)	\(1\)		\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)

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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.