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 127 matches)

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Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
1512.1.e.a	$1$	$0.755$	$\Q$	$\Q(\sqrt{-42}) $	None	$-1$	$0$	$0$	$-1$		$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots$
1512.1.e.b	$1$	$0.755$	$\Q$	$\Q(\sqrt{-42}) $	None	$-1$	$0$	$0$	$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots$
1512.1.e.c	$1$	$0.755$	$\Q$	$\Q(\sqrt{-42}) $	None	$1$	$0$	$0$	$-1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots$
1512.1.e.d	$1$	$0.755$	$\Q$	$\Q(\sqrt{-42}) $	None	$1$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots$
1512.1.l.a	$4$	$0.755$	$\Q(\zeta_{12})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$-2$		$q-\zeta_{12}^{3}q^{2}-q^{4}+(\zeta_{12}-\zeta_{12}^{5})q^{5}+\cdots$
1512.1.ba.a	$4$	$0.755$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$
1512.1.bd.a	$2$	$0.755$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-6}) $	None	$-1$	$0$	$-2$	$-1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
1512.1.bd.b	$2$	$0.755$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-6}) $	None	$-1$	$0$	$1$	$2$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{7}+\cdots$
1512.1.bd.c	$2$	$0.755$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-6}) $	None	$1$	$0$	$-1$	$2$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\cdots$
1512.1.bd.d	$2$	$0.755$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-6}) $	None	$1$	$0$	$2$	$-1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
1512.1.bn.a	$2$	$0.755$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-14}) $	None	$1$	$0$	$-1$	$-1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
1512.1.bn.b	$2$	$0.755$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-14}) $	None	$1$	$0$	$1$	$-1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
1512.1.bn.c	$4$	$0.755$	$\Q(\zeta_{12})$	$\Q(\sqrt{-14}) $	None	$-2$	$0$	$0$	$2$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
1512.1.bw.a	$4$	$0.755$	$\Q(\zeta_{12})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$-2$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{7}+\cdots$
1512.1.bw.b	$4$	$0.755$	$\Q(\zeta_{12})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$4$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
1512.1.ce.a	$4$	$0.755$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
1512.1.cu.a	$4$	$0.755$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$-2$		$q+\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{17}+(-1+\cdots)q^{19}+\cdots$
1512.1.ef.a	$6$	$0.755$	$\Q(\zeta_{18})$	$\Q(\sqrt{-14}) $	None	$0$	$-3$	$6$	$0$		$q-\zeta_{18}^{5}q^{2}+\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}+(1+\cdots)q^{5}+\cdots$
1512.1.ef.b	$6$	$0.755$	$\Q(\zeta_{18})$	$\Q(\sqrt{-14}) $	None	$0$	$3$	$-6$	$0$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}+(-1+\cdots)q^{5}+\cdots$
1512.1.ef.c	$12$	$0.755$	$\Q(\zeta_{36})$	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{36}^{10}q^{2}+\zeta_{36}^{3}q^{3}-\zeta_{36}^{2}q^{4}+\cdots$
1512.2.a.a	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$-4$	$-1$	$-$	$q-4q^{5}-q^{7}-4q^{11}-q^{13}-3q^{17}+\cdots$
1512.2.a.b	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$-1$	$-1$	$-$	$q-q^{5}-q^{7}-6q^{11}+4q^{13}+3q^{17}+\cdots$
1512.2.a.c	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$-1$	$-1$	$-$	$q-q^{5}-q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots$
1512.2.a.d	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$-1$	$-1$	$+$	$q-q^{5}-q^{7}+2q^{11}-4q^{13}+3q^{17}+\cdots$
1512.2.a.e	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$-1$	$1$	$+$	$q-q^{5}+q^{7}-3q^{11}-2q^{17}+q^{19}+\cdots$
1512.2.a.f	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$-1$	$1$	$+$	$q-q^{5}+q^{7}-6q^{13}+7q^{17}-8q^{19}+\cdots$
1512.2.a.g	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$1$	$-1$	$+$	$q+q^{5}-q^{7}-2q^{11}-4q^{13}-3q^{17}+\cdots$
1512.2.a.h	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$1$	$-1$	$+$	$q+q^{5}-q^{7}+q^{11}-4q^{13}-6q^{17}+\cdots$
1512.2.a.i	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$1$	$-1$	$-$	$q+q^{5}-q^{7}+6q^{11}+4q^{13}-3q^{17}+\cdots$
1512.2.a.j	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$1$	$1$	$+$	$q+q^{5}+q^{7}-6q^{13}-7q^{17}-8q^{19}+\cdots$
1512.2.a.k	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$1$	$1$	$-$	$q+q^{5}+q^{7}+3q^{11}+2q^{17}+q^{19}+\cdots$
1512.2.a.l	$1$	$12.073$	$\Q$	None	None	$0$	$0$	$4$	$-1$	$-$	$q+4q^{5}-q^{7}+4q^{11}-q^{13}+3q^{17}+\cdots$
1512.2.a.m	$2$	$12.073$	$\Q(\sqrt{3}) $	None	None	$0$	$0$	$-4$	$2$	$+$	$q+(-2+\beta )q^{5}+q^{7}-3\beta q^{11}+2\beta q^{13}+\cdots$
1512.2.a.n	$2$	$12.073$	$\Q(\sqrt{33}) $	None	None	$0$	$0$	$-1$	$2$	$-$	$q-\beta q^{5}+q^{7}+(1+\beta )q^{13}-q^{17}+(2+\cdots)q^{19}+\cdots$
1512.2.a.o	$2$	$12.073$	$\Q(\sqrt{7}) $	None	None	$0$	$0$	$0$	$-2$	$+$	$q+\beta q^{5}-q^{7}+(-2-\beta )q^{11}-2\beta q^{13}+\cdots$
1512.2.a.p	$2$	$12.073$	$\Q(\sqrt{7}) $	None	None	$0$	$0$	$0$	$-2$	$-$	$q+\beta q^{5}-q^{7}+(2-\beta )q^{11}+2\beta q^{13}+\cdots$
1512.2.a.q	$2$	$12.073$	$\Q(\sqrt{33}) $	None	None	$0$	$0$	$1$	$2$	$-$	$q+\beta q^{5}+q^{7}+(1+\beta )q^{13}+q^{17}+(2+\cdots)q^{19}+\cdots$
1512.2.a.r	$2$	$12.073$	$\Q(\sqrt{3}) $	None	None	$0$	$0$	$4$	$2$	$-$	$q+(2+\beta )q^{5}+q^{7}-3\beta q^{11}-2\beta q^{13}+\cdots$
1512.2.c.a	$2$	$12.073$	$\Q(\sqrt{-1}) $	None	None	$-2$	$0$	$0$	$-2$		$q+(-1-i)q^{2}+2iq^{4}+2iq^{5}-q^{7}+\cdots$
1512.2.c.b	$2$	$12.073$	$\Q(\sqrt{-1}) $	None	None	$2$	$0$	$0$	$-2$		$q+(1-i)q^{2}-2iq^{4}+2iq^{5}-q^{7}+\cdots$
1512.2.c.c	$8$	$12.073$	8.0.3317760000.5	None	None	$0$	$0$	$0$	$-8$		$q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots$
1512.2.c.d	$16$	$12.073$	$\Q(\zeta_{40})$	None	None	$0$	$0$	$0$	$-16$		$q+\zeta_{40}^{11}q^{2}-\zeta_{40}q^{4}+(\zeta_{40}^{10}+\zeta_{40}^{11}+\cdots)q^{5}+\cdots$
1512.2.c.e	$20$	$12.073$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$0$	$0$	$-20$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{14}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots$
1512.2.c.f	$24$	$12.073$		None	None	$0$	$0$	$0$	$24$
1512.2.c.g	$24$	$12.073$		None	None	$0$	$0$	$0$	$24$
1512.2.j.a	$8$	$12.073$	8.0.56070144.2	None	None	$-4$	$0$	$-8$	$0$		$q+(-1-\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
1512.2.j.b	$8$	$12.073$	8.0.56070144.2	None	None	$4$	$0$	$8$	$0$		$q+(1+\beta _{3}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
1512.2.j.c	$32$	$12.073$		None	None	$0$	$0$	$0$	$0$
1512.2.j.d	$48$	$12.073$		None	None	$0$	$0$	$0$	$0$
1512.2.k.a	$16$	$12.073$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$-2$		$q-\beta _{9}q^{5}-\beta _{1}q^{7}-\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots$

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Label	Dim.	\(A\)	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
1512.1.e.a	\(1\)	\(0.755\)	\(\Q\)	\(\Q(\sqrt{-42}) \)	None	\(-1\)	\(0\)	\(0\)	\(-1\)		\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots\)
1512.1.e.b	\(1\)	\(0.755\)	\(\Q\)	\(\Q(\sqrt{-42}) \)	None	\(-1\)	\(0\)	\(0\)	\(1\)		\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots\)
1512.1.e.c	\(1\)	\(0.755\)	\(\Q\)	\(\Q(\sqrt{-42}) \)	None	\(1\)	\(0\)	\(0\)	\(-1\)		\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)
1512.1.e.d	\(1\)	\(0.755\)	\(\Q\)	\(\Q(\sqrt{-42}) \)	None	\(1\)	\(0\)	\(0\)	\(1\)		\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots\)
1512.1.l.a	\(4\)	\(0.755\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-\zeta_{12}^{3}q^{2}-q^{4}+(\zeta_{12}-\zeta_{12}^{5})q^{5}+\cdots\)
1512.1.ba.a	\(4\)	\(0.755\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
1512.1.bd.a	\(2\)	\(0.755\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-6}) \)	None	\(-1\)	\(0\)	\(-2\)	\(-1\)		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)
1512.1.bd.b	\(2\)	\(0.755\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-6}) \)	None	\(-1\)	\(0\)	\(1\)	\(2\)		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
1512.1.bd.c	\(2\)	\(0.755\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-6}) \)	None	\(1\)	\(0\)	\(-1\)	\(2\)		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
1512.1.bd.d	\(2\)	\(0.755\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-6}) \)	None	\(1\)	\(0\)	\(2\)	\(-1\)		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)
1512.1.bn.a	\(2\)	\(0.755\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-14}) \)	None	\(1\)	\(0\)	\(-1\)	\(-1\)		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
1512.1.bn.b	\(2\)	\(0.755\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-14}) \)	None	\(1\)	\(0\)	\(1\)	\(-1\)		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
1512.1.bn.c	\(4\)	\(0.755\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-14}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)		\(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)
1512.1.bw.a	\(4\)	\(0.755\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{7}+\cdots\)
1512.1.bw.b	\(4\)	\(0.755\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)
1512.1.ce.a	\(4\)	\(0.755\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1512.1.cu.a	\(4\)	\(0.755\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{17}+(-1+\cdots)q^{19}+\cdots\)
1512.1.ef.a	\(6\)	\(0.755\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(-3\)	\(6\)	\(0\)		\(q-\zeta_{18}^{5}q^{2}+\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}+(1+\cdots)q^{5}+\cdots\)
1512.1.ef.b	\(6\)	\(0.755\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(3\)	\(-6\)	\(0\)		\(q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1512.1.ef.c	\(12\)	\(0.755\)	\(\Q(\zeta_{36})\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{36}^{10}q^{2}+\zeta_{36}^{3}q^{3}-\zeta_{36}^{2}q^{4}+\cdots\)
1512.2.a.a	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-4\)	\(-1\)	\(-\)	\(q-4q^{5}-q^{7}-4q^{11}-q^{13}-3q^{17}+\cdots\)
1512.2.a.b	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(-1\)	\(-\)	\(q-q^{5}-q^{7}-6q^{11}+4q^{13}+3q^{17}+\cdots\)
1512.2.a.c	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(-1\)	\(-\)	\(q-q^{5}-q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots\)
1512.2.a.d	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(-1\)	\(+\)	\(q-q^{5}-q^{7}+2q^{11}-4q^{13}+3q^{17}+\cdots\)
1512.2.a.e	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(1\)	\(+\)	\(q-q^{5}+q^{7}-3q^{11}-2q^{17}+q^{19}+\cdots\)
1512.2.a.f	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(1\)	\(+\)	\(q-q^{5}+q^{7}-6q^{13}+7q^{17}-8q^{19}+\cdots\)
1512.2.a.g	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(-1\)	\(+\)	\(q+q^{5}-q^{7}-2q^{11}-4q^{13}-3q^{17}+\cdots\)
1512.2.a.h	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(-1\)	\(+\)	\(q+q^{5}-q^{7}+q^{11}-4q^{13}-6q^{17}+\cdots\)
1512.2.a.i	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(-1\)	\(-\)	\(q+q^{5}-q^{7}+6q^{11}+4q^{13}-3q^{17}+\cdots\)
1512.2.a.j	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(1\)	\(+\)	\(q+q^{5}+q^{7}-6q^{13}-7q^{17}-8q^{19}+\cdots\)
1512.2.a.k	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(1\)	\(-\)	\(q+q^{5}+q^{7}+3q^{11}+2q^{17}+q^{19}+\cdots\)
1512.2.a.l	\(1\)	\(12.073\)	\(\Q\)	None	None	\(0\)	\(0\)	\(4\)	\(-1\)	\(-\)	\(q+4q^{5}-q^{7}+4q^{11}-q^{13}+3q^{17}+\cdots\)
1512.2.a.m	\(2\)	\(12.073\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(2\)	\(+\)	\(q+(-2+\beta )q^{5}+q^{7}-3\beta q^{11}+2\beta q^{13}+\cdots\)
1512.2.a.n	\(2\)	\(12.073\)	\(\Q(\sqrt{33}) \)	None	None	\(0\)	\(0\)	\(-1\)	\(2\)	\(-\)	\(q-\beta q^{5}+q^{7}+(1+\beta )q^{13}-q^{17}+(2+\cdots)q^{19}+\cdots\)
1512.2.a.o	\(2\)	\(12.073\)	\(\Q(\sqrt{7}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(q+\beta q^{5}-q^{7}+(-2-\beta )q^{11}-2\beta q^{13}+\cdots\)
1512.2.a.p	\(2\)	\(12.073\)	\(\Q(\sqrt{7}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(q+\beta q^{5}-q^{7}+(2-\beta )q^{11}+2\beta q^{13}+\cdots\)
1512.2.a.q	\(2\)	\(12.073\)	\(\Q(\sqrt{33}) \)	None	None	\(0\)	\(0\)	\(1\)	\(2\)	\(-\)	\(q+\beta q^{5}+q^{7}+(1+\beta )q^{13}+q^{17}+(2+\cdots)q^{19}+\cdots\)
1512.2.a.r	\(2\)	\(12.073\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(0\)	\(4\)	\(2\)	\(-\)	\(q+(2+\beta )q^{5}+q^{7}-3\beta q^{11}-2\beta q^{13}+\cdots\)
1512.2.c.a	\(2\)	\(12.073\)	\(\Q(\sqrt{-1}) \)	None	None	\(-2\)	\(0\)	\(0\)	\(-2\)		\(q+(-1-i)q^{2}+2iq^{4}+2iq^{5}-q^{7}+\cdots\)
1512.2.c.b	\(2\)	\(12.073\)	\(\Q(\sqrt{-1}) \)	None	None	\(2\)	\(0\)	\(0\)	\(-2\)		\(q+(1-i)q^{2}-2iq^{4}+2iq^{5}-q^{7}+\cdots\)
1512.2.c.c	\(8\)	\(12.073\)	8.0.3317760000.5	None	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
1512.2.c.d	\(16\)	\(12.073\)	\(\Q(\zeta_{40})\)	None	None	\(0\)	\(0\)	\(0\)	\(-16\)		\(q+\zeta_{40}^{11}q^{2}-\zeta_{40}q^{4}+(\zeta_{40}^{10}+\zeta_{40}^{11}+\cdots)q^{5}+\cdots\)
1512.2.c.e	\(20\)	\(12.073\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(-20\)		\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{14}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots\)
1512.2.c.f	\(24\)	\(12.073\)		None	None	\(0\)	\(0\)	\(0\)	\(24\)
1512.2.c.g	\(24\)	\(12.073\)		None	None	\(0\)	\(0\)	\(0\)	\(24\)
1512.2.j.a	\(8\)	\(12.073\)	8.0.56070144.2	None	None	\(-4\)	\(0\)	\(-8\)	\(0\)		\(q+(-1-\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
1512.2.j.b	\(8\)	\(12.073\)	8.0.56070144.2	None	None	\(4\)	\(0\)	\(8\)	\(0\)		\(q+(1+\beta _{3}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
1512.2.j.c	\(32\)	\(12.073\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
1512.2.j.d	\(48\)	\(12.073\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
1512.2.k.a	\(16\)	\(12.073\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-\beta _{9}q^{5}-\beta _{1}q^{7}-\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots\)

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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.