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 107 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
1960.1.i.a	$1$	$0.978$	$\Q$	$\Q(\sqrt{-10}) $	None	$-1$	$0$	$-1$	$0$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots$
1960.1.i.b	$1$	$0.978$	$\Q$	$\Q(\sqrt{-10}) $	None	$-1$	$0$	$1$	$0$		$q-q^{2}+q^{4}+q^{5}-q^{8}+q^{9}-q^{10}+\cdots$
1960.1.i.c	$1$	$0.978$	$\Q$	$\Q(\sqrt{-10}) $	None	$1$	$0$	$-1$	$0$		$q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots$
1960.1.i.d	$1$	$0.978$	$\Q$	$\Q(\sqrt{-10}) $	None	$1$	$0$	$1$	$0$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{9}+q^{10}+\cdots$
1960.1.u.a	$8$	$0.978$	$\Q(\zeta_{16})$	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{16}^{2}q^{2}+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}+\zeta_{16}^{4}q^{4}+\cdots$
1960.1.v.a	$4$	$0.978$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}q^{3}-\zeta_{8}q^{5}+q^{11}+\zeta_{8}q^{13}+\cdots$
1960.1.bi.a	$2$	$0.978$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-10}) $	None	$-1$	$0$	$1$	$0$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots$
1960.1.bi.b	$2$	$0.978$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-10}) $	None	$1$	$0$	$-1$	$0$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{8}-\zeta_{6}q^{9}+\cdots$
1960.1.bk.a	$8$	$0.978$	$\Q(\zeta_{24})$	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}^{2}q^{2}+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
1960.1.br.a	$8$	$0.978$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{11}q^{5}-\zeta_{24}^{4}q^{11}+\cdots$
1960.1.bu.a	$16$	$0.978$	$\Q(\zeta_{48})$	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{48}^{2}q^{2}+(-\zeta_{48}-\zeta_{48}^{19})q^{3}+\cdots$
1960.1.cf.a	$6$	$0.978$	$\Q(\zeta_{14})$	$\Q(\sqrt{-10}) $	None	$-1$	$0$	$-1$	$-1$		$q-\zeta_{14}^{5}q^{2}-\zeta_{14}^{3}q^{4}-\zeta_{14}q^{5}+\zeta_{14}^{6}q^{7}+\cdots$
1960.1.cf.b	$6$	$0.978$	$\Q(\zeta_{14})$	$\Q(\sqrt{-10}) $	None	$1$	$0$	$1$	$1$		$q+\zeta_{14}^{5}q^{2}-\zeta_{14}^{3}q^{4}+\zeta_{14}q^{5}-\zeta_{14}^{6}q^{7}+\cdots$
1960.1.cz.a	$12$	$0.978$	$\Q(\zeta_{21})$	$\Q(\sqrt{-10}) $	None	$-1$	$0$	$-1$	$2$		$q-\zeta_{42}^{16}q^{2}-\zeta_{42}^{11}q^{4}+\zeta_{42}^{13}q^{5}+\cdots$
1960.1.cz.b	$12$	$0.978$	$\Q(\zeta_{21})$	$\Q(\sqrt{-10}) $	None	$1$	$0$	$1$	$-2$		$q+\zeta_{42}^{16}q^{2}-\zeta_{42}^{11}q^{4}-\zeta_{42}^{13}q^{5}+\cdots$
1960.2.a.a	$1$	$15.651$	$\Q$	None	None	$0$	$-2$	$-1$	$0$	$-$	$q-2q^{3}-q^{5}+q^{9}-q^{11}-3q^{13}+\cdots$
1960.2.a.b	$1$	$15.651$	$\Q$	None	None	$0$	$-2$	$-1$	$0$	$+$	$q-2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
1960.2.a.c	$1$	$15.651$	$\Q$	None	None	$0$	$-1$	$-1$	$0$	$+$	$q-q^{3}-q^{5}-2q^{9}-2q^{11}+4q^{13}+\cdots$
1960.2.a.d	$1$	$15.651$	$\Q$	None	None	$0$	$-1$	$1$	$0$	$-$	$q-q^{3}+q^{5}-2q^{9}-5q^{11}-7q^{13}+\cdots$
1960.2.a.e	$1$	$15.651$	$\Q$	None	None	$0$	$-1$	$1$	$0$	$-$	$q-q^{3}+q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots$
1960.2.a.f	$1$	$15.651$	$\Q$	None	None	$0$	$-1$	$1$	$0$	$+$	$q-q^{3}+q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots$
1960.2.a.g	$1$	$15.651$	$\Q$	None	None	$0$	$0$	$-1$	$0$	$-$	$q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots$
1960.2.a.h	$1$	$15.651$	$\Q$	None	None	$0$	$1$	$-1$	$0$	$+$	$q+q^{3}-q^{5}-2q^{9}-5q^{11}+7q^{13}+\cdots$
1960.2.a.i	$1$	$15.651$	$\Q$	None	None	$0$	$1$	$-1$	$0$	$-$	$q+q^{3}-q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots$
1960.2.a.j	$1$	$15.651$	$\Q$	None	None	$0$	$1$	$-1$	$0$	$-$	$q+q^{3}-q^{5}-2q^{9}+3q^{11}-q^{13}+\cdots$
1960.2.a.k	$1$	$15.651$	$\Q$	None	None	$0$	$1$	$1$	$0$	$+$	$q+q^{3}+q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots$
1960.2.a.l	$1$	$15.651$	$\Q$	None	None	$0$	$1$	$1$	$0$	$+$	$q+q^{3}+q^{5}-2q^{9}-2q^{11}-4q^{13}+\cdots$
1960.2.a.m	$1$	$15.651$	$\Q$	None	None	$0$	$2$	$1$	$0$	$-$	$q+2q^{3}+q^{5}+q^{9}-q^{11}+3q^{13}+\cdots$
1960.2.a.n	$1$	$15.651$	$\Q$	None	None	$0$	$2$	$1$	$0$	$-$	$q+2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
1960.2.a.o	$1$	$15.651$	$\Q$	None	None	$0$	$3$	$-1$	$0$	$-$	$q+3q^{3}-q^{5}+6q^{9}-5q^{11}+5q^{13}+\cdots$
1960.2.a.p	$2$	$15.651$	$\Q(\sqrt{2}) $	None	None	$0$	$-2$	$2$	$0$	$+$	$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots$
1960.2.a.q	$2$	$15.651$	$\Q(\sqrt{2}) $	None	None	$0$	$-2$	$2$	$0$	$+$	$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}-q^{11}+\cdots$
1960.2.a.r	$2$	$15.651$	$\Q(\sqrt{17}) $	None	None	$0$	$-1$	$-2$	$0$	$+$	$q-\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
1960.2.a.s	$2$	$15.651$	$\Q(\sqrt{33}) $	None	None	$0$	$1$	$2$	$0$	$-$	$q+\beta q^{3}+q^{5}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots$
1960.2.a.t	$2$	$15.651$	$\Q(\sqrt{2}) $	None	None	$0$	$2$	$-2$	$0$	$+$	$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots$
1960.2.a.u	$2$	$15.651$	$\Q(\sqrt{2}) $	None	None	$0$	$2$	$-2$	$0$	$-$	$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots$
1960.2.a.v	$3$	$15.651$	3.3.1944.1	None	None	$0$	$0$	$-3$	$0$	$-$	$q+\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
1960.2.a.w	$3$	$15.651$	3.3.1944.1	None	None	$0$	$0$	$3$	$0$	$-$	$q-\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
1960.2.a.x	$4$	$15.651$	4.4.16448.2	None	None	$0$	$-2$	$-4$	$0$	$+$	$q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1960.2.a.y	$4$	$15.651$	4.4.16448.2	None	None	$0$	$2$	$4$	$0$	$-$	$q+\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1960.2.g.a	$2$	$15.651$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-4$	$0$		$q+iq^{3}+(-2-i)q^{5}+2q^{9}-q^{11}+\cdots$
1960.2.g.b	$2$	$15.651$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$2$	$0$		$q+iq^{3}+(1-i)q^{5}-q^{9}-4q^{11}+2iq^{13}+\cdots$
1960.2.g.c	$6$	$15.651$	6.0.5161984.1	None	None	$0$	$0$	$0$	$0$		$q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$
1960.2.g.d	$8$	$15.651$	8.0.$\cdots$.3	None	None	$0$	$0$	$0$	$0$		$q+\beta _{5}q^{3}-\beta _{6}q^{5}-\beta _{2}q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots$
1960.2.g.e	$12$	$15.651$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$
1960.2.g.f	$12$	$15.651$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}-\beta _{5}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$
1960.2.g.g	$20$	$15.651$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{17}q^{3}-\beta _{16}q^{5}+(-1+\beta _{1})q^{9}+\cdots$
1960.2.q.a	$2$	$15.651$	$\Q(\sqrt{-3}) $	None	None	$0$	$-3$	$1$	$0$		$q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$
1960.2.q.b	$2$	$15.651$	$\Q(\sqrt{-3}) $	None	None	$0$	$-2$	$-1$	$0$		$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
1960.2.q.c	$2$	$15.651$	$\Q(\sqrt{-3}) $	None	None	$0$	$-2$	$-1$	$0$		$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$

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Elliptic curves over $\Q$
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Higher genus families
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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
1960.1.i.a	\(1\)	\(0.978\)	\(\Q\)	\(\Q(\sqrt{-10}) \)	None	\(-1\)	\(0\)	\(-1\)	\(0\)		\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots\)
1960.1.i.b	\(1\)	\(0.978\)	\(\Q\)	\(\Q(\sqrt{-10}) \)	None	\(-1\)	\(0\)	\(1\)	\(0\)		\(q-q^{2}+q^{4}+q^{5}-q^{8}+q^{9}-q^{10}+\cdots\)
1960.1.i.c	\(1\)	\(0.978\)	\(\Q\)	\(\Q(\sqrt{-10}) \)	None	\(1\)	\(0\)	\(-1\)	\(0\)		\(q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots\)
1960.1.i.d	\(1\)	\(0.978\)	\(\Q\)	\(\Q(\sqrt{-10}) \)	None	\(1\)	\(0\)	\(1\)	\(0\)		\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{9}+q^{10}+\cdots\)
1960.1.u.a	\(8\)	\(0.978\)	\(\Q(\zeta_{16})\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{16}^{2}q^{2}+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
1960.1.v.a	\(4\)	\(0.978\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}q^{3}-\zeta_{8}q^{5}+q^{11}+\zeta_{8}q^{13}+\cdots\)
1960.1.bi.a	\(2\)	\(0.978\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-10}) \)	None	\(-1\)	\(0\)	\(1\)	\(0\)		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots\)
1960.1.bi.b	\(2\)	\(0.978\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-10}) \)	None	\(1\)	\(0\)	\(-1\)	\(0\)		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{8}-\zeta_{6}q^{9}+\cdots\)
1960.1.bk.a	\(8\)	\(0.978\)	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}^{2}q^{2}+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
1960.1.br.a	\(8\)	\(0.978\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{11}q^{5}-\zeta_{24}^{4}q^{11}+\cdots\)
1960.1.bu.a	\(16\)	\(0.978\)	\(\Q(\zeta_{48})\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{48}^{2}q^{2}+(-\zeta_{48}-\zeta_{48}^{19})q^{3}+\cdots\)
1960.1.cf.a	\(6\)	\(0.978\)	\(\Q(\zeta_{14})\)	\(\Q(\sqrt{-10}) \)	None	\(-1\)	\(0\)	\(-1\)	\(-1\)		\(q-\zeta_{14}^{5}q^{2}-\zeta_{14}^{3}q^{4}-\zeta_{14}q^{5}+\zeta_{14}^{6}q^{7}+\cdots\)
1960.1.cf.b	\(6\)	\(0.978\)	\(\Q(\zeta_{14})\)	\(\Q(\sqrt{-10}) \)	None	\(1\)	\(0\)	\(1\)	\(1\)		\(q+\zeta_{14}^{5}q^{2}-\zeta_{14}^{3}q^{4}+\zeta_{14}q^{5}-\zeta_{14}^{6}q^{7}+\cdots\)
1960.1.cz.a	\(12\)	\(0.978\)	\(\Q(\zeta_{21})\)	\(\Q(\sqrt{-10}) \)	None	\(-1\)	\(0\)	\(-1\)	\(2\)		\(q-\zeta_{42}^{16}q^{2}-\zeta_{42}^{11}q^{4}+\zeta_{42}^{13}q^{5}+\cdots\)
1960.1.cz.b	\(12\)	\(0.978\)	\(\Q(\zeta_{21})\)	\(\Q(\sqrt{-10}) \)	None	\(1\)	\(0\)	\(1\)	\(-2\)		\(q+\zeta_{42}^{16}q^{2}-\zeta_{42}^{11}q^{4}-\zeta_{42}^{13}q^{5}+\cdots\)
1960.2.a.a	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(-1\)	\(0\)	\(-\)	\(q-2q^{3}-q^{5}+q^{9}-q^{11}-3q^{13}+\cdots\)
1960.2.a.b	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(-1\)	\(0\)	\(+\)	\(q-2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1960.2.a.c	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(+\)	\(q-q^{3}-q^{5}-2q^{9}-2q^{11}+4q^{13}+\cdots\)
1960.2.a.d	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(1\)	\(0\)	\(-\)	\(q-q^{3}+q^{5}-2q^{9}-5q^{11}-7q^{13}+\cdots\)
1960.2.a.e	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(1\)	\(0\)	\(-\)	\(q-q^{3}+q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots\)
1960.2.a.f	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(1\)	\(0\)	\(+\)	\(q-q^{3}+q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots\)
1960.2.a.g	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(0\)	\(-\)	\(q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
1960.2.a.h	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-1\)	\(0\)	\(+\)	\(q+q^{3}-q^{5}-2q^{9}-5q^{11}+7q^{13}+\cdots\)
1960.2.a.i	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-1\)	\(0\)	\(-\)	\(q+q^{3}-q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots\)
1960.2.a.j	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-1\)	\(0\)	\(-\)	\(q+q^{3}-q^{5}-2q^{9}+3q^{11}-q^{13}+\cdots\)
1960.2.a.k	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(1\)	\(1\)	\(0\)	\(+\)	\(q+q^{3}+q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots\)
1960.2.a.l	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(1\)	\(1\)	\(0\)	\(+\)	\(q+q^{3}+q^{5}-2q^{9}-2q^{11}-4q^{13}+\cdots\)
1960.2.a.m	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(2\)	\(1\)	\(0\)	\(-\)	\(q+2q^{3}+q^{5}+q^{9}-q^{11}+3q^{13}+\cdots\)
1960.2.a.n	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(2\)	\(1\)	\(0\)	\(-\)	\(q+2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1960.2.a.o	\(1\)	\(15.651\)	\(\Q\)	None	None	\(0\)	\(3\)	\(-1\)	\(0\)	\(-\)	\(q+3q^{3}-q^{5}+6q^{9}-5q^{11}+5q^{13}+\cdots\)
1960.2.a.p	\(2\)	\(15.651\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(+\)	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
1960.2.a.q	\(2\)	\(15.651\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(+\)	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}-q^{11}+\cdots\)
1960.2.a.r	\(2\)	\(15.651\)	\(\Q(\sqrt{17}) \)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(+\)	\(q-\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
1960.2.a.s	\(2\)	\(15.651\)	\(\Q(\sqrt{33}) \)	None	None	\(0\)	\(1\)	\(2\)	\(0\)	\(-\)	\(q+\beta q^{3}+q^{5}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
1960.2.a.t	\(2\)	\(15.651\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(+\)	\(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots\)
1960.2.a.u	\(2\)	\(15.651\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
1960.2.a.v	\(3\)	\(15.651\)	3.3.1944.1	None	None	\(0\)	\(0\)	\(-3\)	\(0\)	\(-\)	\(q+\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
1960.2.a.w	\(3\)	\(15.651\)	3.3.1944.1	None	None	\(0\)	\(0\)	\(3\)	\(0\)	\(-\)	\(q-\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
1960.2.a.x	\(4\)	\(15.651\)	4.4.16448.2	None	None	\(0\)	\(-2\)	\(-4\)	\(0\)	\(+\)	\(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1960.2.a.y	\(4\)	\(15.651\)	4.4.16448.2	None	None	\(0\)	\(2\)	\(4\)	\(0\)	\(-\)	\(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1960.2.g.a	\(2\)	\(15.651\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+iq^{3}+(-2-i)q^{5}+2q^{9}-q^{11}+\cdots\)
1960.2.g.b	\(2\)	\(15.651\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+iq^{3}+(1-i)q^{5}-q^{9}-4q^{11}+2iq^{13}+\cdots\)
1960.2.g.c	\(6\)	\(15.651\)	6.0.5161984.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.g.d	\(8\)	\(15.651\)	8.0.\(\cdots\).3	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{5}q^{3}-\beta _{6}q^{5}-\beta _{2}q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
1960.2.g.e	\(12\)	\(15.651\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
1960.2.g.f	\(12\)	\(15.651\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}-\beta _{5}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
1960.2.g.g	\(20\)	\(15.651\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{17}q^{3}-\beta _{16}q^{5}+(-1+\beta _{1})q^{9}+\cdots\)
1960.2.q.a	\(2\)	\(15.651\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-3\)	\(1\)	\(0\)		\(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
1960.2.q.b	\(2\)	\(15.651\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-2\)	\(-1\)	\(0\)		\(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1960.2.q.c	\(2\)	\(15.651\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-2\)	\(-1\)	\(0\)		\(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)

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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.