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 203 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
2016.1.e.a	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+(-\zeta_{8}+\cdots)q^{23}+\cdots$
2016.1.f.a	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-21}) $	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots$
2016.1.l.a	$1$	$1.006$	$\Q$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	$0$	$0$	$0$	$1$		$q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots$
2016.1.l.b	$2$	$1.006$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{42}) $	$0$	$0$	$0$	$-2$		$q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots$
2016.1.bi.a	$4$	$1.006$	$\Q(\zeta_{12})$	None	None	$0$	$-2$	$0$	$0$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
2016.1.bv.a	$2$	$1.006$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-14}) $	None	$0$	$-2$	$1$	$1$		$q-q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
2016.1.bv.b	$2$	$1.006$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-14}) $	None	$0$	$2$	$-1$	$1$		$q+q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
2016.1.bv.c	$4$	$1.006$	$\Q(\zeta_{12})$	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$-2$		$q-\zeta_{12}^{3}q^{3}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\zeta_{12}^{4}q^{7}+\cdots$
2016.1.bw.a	$4$	$1.006$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$0$		$q-\zeta_{12}q^{3}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots$
2016.1.cd.a	$4$	$1.006$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$2$	$0$		$q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots$
2016.1.ce.a	$4$	$1.006$	$\Q(\zeta_{12})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$2$		$q+(\zeta_{12}^{3}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{7}+\zeta_{12}^{5}q^{11}+\cdots$
2016.1.cm.a	$4$	$1.006$	$\Q(\zeta_{12})$	None	None	$0$	$4$	$0$	$0$		$q+q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+q^{9}+\cdots$
2016.1.dd.a	$4$	$1.006$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$0$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{7}-q^{9}-\zeta_{12}^{2}q^{13}+\cdots$
2016.1.dn.a	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$-4$	$0$	$0$	$0$		$q-q^{2}+q^{4}+\zeta_{8}^{3}q^{7}-q^{8}+(-\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
2016.1.dn.b	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{8}+\cdots$
2016.1.dn.c	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\cdots$
2016.1.dn.d	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$4$	$0$	$0$	$0$		$q+q^{2}+q^{4}+\zeta_{8}^{3}q^{7}+q^{8}+(\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
2016.1.dp.a	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
2016.1.dp.b	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}q^{8}+\cdots$
2016.1.dp.c	$4$	$1.006$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
2016.2.a.a	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$-2$	$-1$	$-$	$q-2q^{5}-q^{7}+2q^{13}-2q^{17}+4q^{19}+\cdots$
2016.2.a.b	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$-2$	$1$	$+$	$q-2q^{5}+q^{7}+2q^{13}-2q^{17}-4q^{19}+\cdots$
2016.2.a.c	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$0$	$-1$	$+$	$q-q^{7}-4q^{11}+2q^{13}+4q^{17}-4q^{23}+\cdots$
2016.2.a.d	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$0$	$-1$	$+$	$q-q^{7}+2q^{11}-2q^{13}-4q^{17}-4q^{19}+\cdots$
2016.2.a.e	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$0$	$-1$	$+$	$q-q^{7}+4q^{11}-4q^{13}+2q^{17}-6q^{19}+\cdots$
2016.2.a.f	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$0$	$-1$	$-$	$q-q^{7}+4q^{11}+2q^{13}-4q^{17}+4q^{23}+\cdots$
2016.2.a.g	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$0$	$1$	$-$	$q+q^{7}-4q^{11}-4q^{13}+2q^{17}+6q^{19}+\cdots$
2016.2.a.h	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$0$	$1$	$+$	$q+q^{7}-4q^{11}+2q^{13}-4q^{17}-4q^{23}+\cdots$
2016.2.a.i	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$0$	$1$	$+$	$q+q^{7}-2q^{11}-2q^{13}-4q^{17}+4q^{19}+\cdots$
2016.2.a.j	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$0$	$1$	$-$	$q+q^{7}+4q^{11}+2q^{13}+4q^{17}+4q^{23}+\cdots$
2016.2.a.k	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$2$	$-1$	$-$	$q+2q^{5}-q^{7}+4q^{11}-6q^{13}+2q^{17}+\cdots$
2016.2.a.l	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$2$	$1$	$+$	$q+2q^{5}+q^{7}-4q^{11}-6q^{13}+2q^{17}+\cdots$
2016.2.a.m	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$4$	$-1$	$-$	$q+4q^{5}-q^{7}-2q^{11}-2q^{13}+4q^{19}+\cdots$
2016.2.a.n	$1$	$16.098$	$\Q$	None	None	$0$	$0$	$4$	$1$	$-$	$q+4q^{5}+q^{7}+2q^{11}-2q^{13}-4q^{19}+\cdots$
2016.2.a.o	$2$	$16.098$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$-2$	$-2$	$-$	$q+(-1-\beta )q^{5}-q^{7}+(-2-2\beta )q^{11}+\cdots$
2016.2.a.p	$2$	$16.098$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$-2$	$-2$	$+$	$q+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots$
2016.2.a.q	$2$	$16.098$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$-2$	$2$	$+$	$q+(-1-\beta )q^{5}+q^{7}+(-1-\beta )q^{11}+\cdots$
2016.2.a.r	$2$	$16.098$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$-2$	$2$	$-$	$q+(-1-\beta )q^{5}+q^{7}+(2+2\beta )q^{11}+\cdots$
2016.2.a.s	$2$	$16.098$	$\Q(\sqrt{3}) $	None	None	$0$	$0$	$0$	$-2$	$+$	$q+\beta q^{5}-q^{7}+(-2-\beta )q^{11}+2q^{13}+\cdots$
2016.2.a.t	$2$	$16.098$	$\Q(\sqrt{3}) $	None	None	$0$	$0$	$0$	$2$	$-$	$q+\beta q^{5}+q^{7}+(2+\beta )q^{11}+2q^{13}+\cdots$
2016.2.a.u	$2$	$16.098$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$2$	$-2$	$-$	$q+(1+\beta )q^{5}-q^{7}+(-1-\beta )q^{11}+2\beta q^{13}+\cdots$
2016.2.a.v	$2$	$16.098$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$2$	$2$	$-$	$q+(1+\beta )q^{5}+q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots$
2016.2.b.a	$8$	$16.098$	8.0.836829184.2	None	None	$0$	$0$	$0$	$-4$		$q-\beta _{1}q^{5}+\beta _{4}q^{7}+(\beta _{2}+\beta _{4}+\beta _{7})q^{11}+\cdots$
2016.2.b.b	$8$	$16.098$	$\Q(\zeta_{16})$	None	None	$0$	$0$	$0$	$0$		$q+\zeta_{16}^{5}q^{5}+\zeta_{16}^{6}q^{7}-\zeta_{16}q^{11}+\cdots$
2016.2.b.c	$8$	$16.098$	8.0.836829184.2	None	None	$0$	$0$	$0$	$4$		$q-\beta _{1}q^{5}-\beta _{4}q^{7}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{11}+\cdots$
2016.2.b.d	$16$	$16.098$	16.0.$\cdots$.7	None	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{5}-\beta _{8}q^{7}+(\beta _{7}+\beta _{11})q^{11}+\cdots$
2016.2.c.a	$2$	$16.098$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$0$	$-2$		$q+\beta q^{5}-q^{7}+2\beta q^{11}-3\beta q^{13}+6q^{17}+\cdots$
2016.2.c.b	$4$	$16.098$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$-4$		$q-\beta _{1}q^{5}-q^{7}+\beta _{1}q^{11}+\beta _{2}q^{17}+\cdots$
2016.2.c.c	$4$	$16.098$	4.0.2312.1	None	None	$0$	$0$	$0$	$4$		$q+\beta _{2}q^{5}+q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\beta _{2}q^{13}+\cdots$
2016.2.c.d	$4$	$16.098$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$4$		$q-\zeta_{12}^{3}q^{5}+q^{7}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{11}+\cdots$

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Elliptic curves over $\Q$
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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
2016.1.e.a	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+(-\zeta_{8}+\cdots)q^{23}+\cdots\)
2016.1.f.a	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
2016.1.l.a	\(1\)	\(1.006\)	\(\Q\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)	\(0\)	\(0\)	\(0\)	\(1\)		\(q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots\)
2016.1.l.b	\(2\)	\(1.006\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{42}) \)	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots\)
2016.1.bi.a	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(-2\)	\(0\)	\(0\)		\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
2016.1.bv.a	\(2\)	\(1.006\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(-2\)	\(1\)	\(1\)		\(q-q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{13}+\cdots\)
2016.1.bv.b	\(2\)	\(1.006\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(2\)	\(-1\)	\(1\)		\(q+q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+q^{9}-\zeta_{6}^{2}q^{13}+\cdots\)
2016.1.bv.c	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-\zeta_{12}^{3}q^{3}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\zeta_{12}^{4}q^{7}+\cdots\)
2016.1.bw.a	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{12}q^{3}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots\)
2016.1.cd.a	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots\)
2016.1.ce.a	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+(\zeta_{12}^{3}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{7}+\zeta_{12}^{5}q^{11}+\cdots\)
2016.1.cm.a	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(4\)	\(0\)	\(0\)		\(q+q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+q^{9}+\cdots\)
2016.1.dd.a	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{7}-q^{9}-\zeta_{12}^{2}q^{13}+\cdots\)
2016.1.dn.a	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}+q^{4}+\zeta_{8}^{3}q^{7}-q^{8}+(-\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
2016.1.dn.b	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{8}+\cdots\)
2016.1.dn.c	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\cdots\)
2016.1.dn.d	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}+\zeta_{8}^{3}q^{7}+q^{8}+(\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
2016.1.dp.a	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
2016.1.dp.b	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}q^{8}+\cdots\)
2016.1.dp.c	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
2016.2.a.a	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(-1\)	\(-\)	\(q-2q^{5}-q^{7}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
2016.2.a.b	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(1\)	\(+\)	\(q-2q^{5}+q^{7}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
2016.2.a.c	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(q-q^{7}-4q^{11}+2q^{13}+4q^{17}-4q^{23}+\cdots\)
2016.2.a.d	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(q-q^{7}+2q^{11}-2q^{13}-4q^{17}-4q^{19}+\cdots\)
2016.2.a.e	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(q-q^{7}+4q^{11}-4q^{13}+2q^{17}-6q^{19}+\cdots\)
2016.2.a.f	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(q-q^{7}+4q^{11}+2q^{13}-4q^{17}+4q^{23}+\cdots\)
2016.2.a.g	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(1\)	\(-\)	\(q+q^{7}-4q^{11}-4q^{13}+2q^{17}+6q^{19}+\cdots\)
2016.2.a.h	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(1\)	\(+\)	\(q+q^{7}-4q^{11}+2q^{13}-4q^{17}-4q^{23}+\cdots\)
2016.2.a.i	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(1\)	\(+\)	\(q+q^{7}-2q^{11}-2q^{13}-4q^{17}+4q^{19}+\cdots\)
2016.2.a.j	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(1\)	\(-\)	\(q+q^{7}+4q^{11}+2q^{13}+4q^{17}+4q^{23}+\cdots\)
2016.2.a.k	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(-1\)	\(-\)	\(q+2q^{5}-q^{7}+4q^{11}-6q^{13}+2q^{17}+\cdots\)
2016.2.a.l	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(1\)	\(+\)	\(q+2q^{5}+q^{7}-4q^{11}-6q^{13}+2q^{17}+\cdots\)
2016.2.a.m	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(4\)	\(-1\)	\(-\)	\(q+4q^{5}-q^{7}-2q^{11}-2q^{13}+4q^{19}+\cdots\)
2016.2.a.n	\(1\)	\(16.098\)	\(\Q\)	None	None	\(0\)	\(0\)	\(4\)	\(1\)	\(-\)	\(q+4q^{5}+q^{7}+2q^{11}-2q^{13}-4q^{19}+\cdots\)
2016.2.a.o	\(2\)	\(16.098\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(-2\)	\(-\)	\(q+(-1-\beta )q^{5}-q^{7}+(-2-2\beta )q^{11}+\cdots\)
2016.2.a.p	\(2\)	\(16.098\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(-2\)	\(+\)	\(q+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots\)
2016.2.a.q	\(2\)	\(16.098\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(2\)	\(+\)	\(q+(-1-\beta )q^{5}+q^{7}+(-1-\beta )q^{11}+\cdots\)
2016.2.a.r	\(2\)	\(16.098\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(2\)	\(-\)	\(q+(-1-\beta )q^{5}+q^{7}+(2+2\beta )q^{11}+\cdots\)
2016.2.a.s	\(2\)	\(16.098\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(q+\beta q^{5}-q^{7}+(-2-\beta )q^{11}+2q^{13}+\cdots\)
2016.2.a.t	\(2\)	\(16.098\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)	\(-\)	\(q+\beta q^{5}+q^{7}+(2+\beta )q^{11}+2q^{13}+\cdots\)
2016.2.a.u	\(2\)	\(16.098\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(2\)	\(-2\)	\(-\)	\(q+(1+\beta )q^{5}-q^{7}+(-1-\beta )q^{11}+2\beta q^{13}+\cdots\)
2016.2.a.v	\(2\)	\(16.098\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(2\)	\(2\)	\(-\)	\(q+(1+\beta )q^{5}+q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots\)
2016.2.b.a	\(8\)	\(16.098\)	8.0.836829184.2	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q-\beta _{1}q^{5}+\beta _{4}q^{7}+(\beta _{2}+\beta _{4}+\beta _{7})q^{11}+\cdots\)
2016.2.b.b	\(8\)	\(16.098\)	\(\Q(\zeta_{16})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{16}^{5}q^{5}+\zeta_{16}^{6}q^{7}-\zeta_{16}q^{11}+\cdots\)
2016.2.b.c	\(8\)	\(16.098\)	8.0.836829184.2	None	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q-\beta _{1}q^{5}-\beta _{4}q^{7}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{11}+\cdots\)
2016.2.b.d	\(16\)	\(16.098\)	16.0.\(\cdots\).7	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{5}-\beta _{8}q^{7}+(\beta _{7}+\beta _{11})q^{11}+\cdots\)
2016.2.c.a	\(2\)	\(16.098\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+\beta q^{5}-q^{7}+2\beta q^{11}-3\beta q^{13}+6q^{17}+\cdots\)
2016.2.c.b	\(4\)	\(16.098\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q-\beta _{1}q^{5}-q^{7}+\beta _{1}q^{11}+\beta _{2}q^{17}+\cdots\)
2016.2.c.c	\(4\)	\(16.098\)	4.0.2312.1	None	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q+\beta _{2}q^{5}+q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\beta _{2}q^{13}+\cdots\)
2016.2.c.d	\(4\)	\(16.098\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q-\zeta_{12}^{3}q^{5}+q^{7}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{11}+\cdots\)

Introduction

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.