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 83 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
1155.1.e.a	$2$	$0.576$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-231}) $	$\Q(\sqrt{165}) $	$0$	$0$	$0$	$0$		$q-iq^{3}+q^{4}-iq^{5}+iq^{7}-q^{9}-q^{11}+\cdots$
1155.1.e.b	$2$	$0.576$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-231}) $	$\Q(\sqrt{165}) $	$0$	$0$	$0$	$0$		$q-iq^{3}+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{11}+\cdots$
1155.1.e.c	$4$	$0.576$	$\Q(\zeta_{12})$	$\Q(\sqrt{-231}) $	None	$0$	$0$	$0$	$0$		$q+(\zeta_{12}^{2}+\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
1155.1.e.d	$4$	$0.576$	$\Q(\zeta_{12})$	$\Q(\sqrt{-231}) $	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+\cdots$
1155.1.ca.a	$8$	$0.576$	$\Q(\zeta_{20})$	$\Q(\sqrt{-35}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{20}^{5}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
1155.1.ca.b	$8$	$0.576$	$\Q(\zeta_{20})$	$\Q(\sqrt{-35}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
1155.2.a.a	$1$	$9.223$	$\Q$	None	None	$-2$	$-1$	$1$	$1$	$+$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots$
1155.2.a.b	$1$	$9.223$	$\Q$	None	None	$-2$	$1$	$-1$	$-1$	$+$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots$
1155.2.a.c	$1$	$9.223$	$\Q$	None	None	$-2$	$1$	$1$	$1$	$+$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
1155.2.a.d	$1$	$9.223$	$\Q$	None	None	$-1$	$-1$	$-1$	$-1$	$+$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
1155.2.a.e	$1$	$9.223$	$\Q$	None	None	$-1$	$-1$	$1$	$-1$	$+$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
1155.2.a.f	$1$	$9.223$	$\Q$	None	None	$-1$	$1$	$1$	$1$	$-$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
1155.2.a.g	$1$	$9.223$	$\Q$	None	None	$0$	$-1$	$-1$	$1$	$+$	$q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+q^{11}+\cdots$
1155.2.a.h	$1$	$9.223$	$\Q$	None	None	$0$	$1$	$-1$	$1$	$+$	$q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-q^{11}+\cdots$
1155.2.a.i	$1$	$9.223$	$\Q$	None	None	$0$	$1$	$1$	$-1$	$+$	$q+q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-q^{11}+\cdots$
1155.2.a.j	$1$	$9.223$	$\Q$	None	None	$1$	$-1$	$-1$	$1$	$-$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
1155.2.a.k	$1$	$9.223$	$\Q$	None	None	$1$	$-1$	$1$	$1$	$+$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
1155.2.a.l	$1$	$9.223$	$\Q$	None	None	$1$	$1$	$-1$	$-1$	$+$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
1155.2.a.m	$1$	$9.223$	$\Q$	None	None	$1$	$1$	$1$	$1$	$-$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
1155.2.a.n	$1$	$9.223$	$\Q$	None	None	$2$	$-1$	$-1$	$-1$	$+$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots$
1155.2.a.o	$2$	$9.223$	$\Q(\sqrt{17}) $	None	None	$-1$	$-2$	$2$	$-2$	$+$	$q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
1155.2.a.p	$2$	$9.223$	$\Q(\sqrt{2}) $	None	None	$0$	$-2$	$-2$	$-2$	$-$	$q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-q^{7}-2\beta q^{8}+\cdots$
1155.2.a.q	$2$	$9.223$	$\Q(\sqrt{6}) $	None	None	$0$	$2$	$2$	$2$	$-$	$q+\beta q^{2}+q^{3}+4q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots$
1155.2.a.r	$2$	$9.223$	$\Q(\sqrt{3}) $	None	None	$2$	$-2$	$-2$	$2$	$-$	$q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots$
1155.2.a.s	$3$	$9.223$	3.3.316.1	None	None	$1$	$-3$	$3$	$-3$	$-$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
1155.2.a.t	$3$	$9.223$	3.3.316.1	None	None	$1$	$3$	$3$	$-3$	$-$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1155.2.a.u	$4$	$9.223$	4.4.13448.1	None	None	$0$	$4$	$-4$	$-4$	$-$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
1155.2.a.v	$4$	$9.223$	4.4.7232.1	None	None	$2$	$-4$	$4$	$4$	$-$	$q-\beta _{2}q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots$
1155.2.a.w	$5$	$9.223$	5.5.352076.1	None	None	$1$	$5$	$-5$	$5$	$-$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
1155.2.c.a	$2$	$9.223$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-4$	$0$		$q+iq^{2}+iq^{3}+q^{4}+(-2+i)q^{5}+\cdots$
1155.2.c.b	$2$	$9.223$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-4$	$0$		$q+iq^{2}+iq^{3}+q^{4}+(-2-i)q^{5}+\cdots$
1155.2.c.c	$6$	$9.223$	6.0.350464.1	None	None	$0$	$0$	$2$	$0$		$q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1155.2.c.d	$6$	$9.223$	6.0.350464.1	None	None	$0$	$0$	$2$	$0$		$q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1155.2.c.e	$20$	$9.223$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$0$	$-2$	$0$		$q+\beta _{1}q^{2}+\beta _{13}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
1155.2.c.f	$20$	$9.223$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$0$	$-2$	$0$		$q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
1155.2.i.a	$8$	$9.223$	8.0.303595776.1	None	None	$0$	$0$	$0$	$0$		$q+(\beta _{1}-\beta _{5})q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+\cdots$
1155.2.i.b	$8$	$9.223$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q+(\zeta_{24}^{4}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
1155.2.i.c	$16$	$9.223$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{8}q^{2}+\beta _{9}q^{3}+(-2-\beta _{3})q^{4}-\beta _{9}q^{5}+\cdots$
1155.2.i.d	$32$	$9.223$		None	None	$0$	$0$	$0$	$0$
1155.2.k.a	$48$	$9.223$		None	None	$0$	$-48$	$4$	$0$
1155.2.k.b	$48$	$9.223$		None	None	$0$	$48$	$-4$	$0$
1155.2.l.a	$4$	$9.223$	$\Q(\zeta_{8})$	None	None	$-4$	$4$	$0$	$0$		$q+(-1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1+\cdots)q^{4}+\cdots$
1155.2.l.b	$4$	$9.223$	$\Q(\zeta_{8})$	None	None	$0$	$4$	$0$	$0$		$q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots$
1155.2.l.c	$4$	$9.223$	$\Q(\zeta_{8})$	None	None	$0$	$4$	$0$	$0$		$q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots$
1155.2.l.d	$4$	$9.223$	$\Q(\zeta_{8})$	None	None	$4$	$4$	$0$	$0$		$q+(1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8}^{3})q^{4}+\cdots$
1155.2.l.e	$40$	$9.223$		None	None	$-4$	$-4$	$0$	$0$
1155.2.l.f	$40$	$9.223$		None	None	$4$	$-4$	$0$	$0$
1155.2.q.a	$2$	$9.223$	$\Q(\sqrt{-3}) $	None	None	$-2$	$-1$	$-1$	$-1$		$q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
1155.2.q.b	$2$	$9.223$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-1$	$-5$		$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$
1155.2.q.c	$2$	$9.223$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-1$	$5$		$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$

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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
1155.1.e.a	\(2\)	\(0.576\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-231}) \)	\(\Q(\sqrt{165}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{3}+q^{4}-iq^{5}+iq^{7}-q^{9}-q^{11}+\cdots\)
1155.1.e.b	\(2\)	\(0.576\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-231}) \)	\(\Q(\sqrt{165}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{3}+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{11}+\cdots\)
1155.1.e.c	\(4\)	\(0.576\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-231}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{12}^{2}+\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
1155.1.e.d	\(4\)	\(0.576\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-231}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+\cdots\)
1155.1.ca.a	\(8\)	\(0.576\)	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-35}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{20}^{5}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
1155.1.ca.b	\(8\)	\(0.576\)	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-35}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
1155.2.a.a	\(1\)	\(9.223\)	\(\Q\)	None	None	\(-2\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
1155.2.a.b	\(1\)	\(9.223\)	\(\Q\)	None	None	\(-2\)	\(1\)	\(-1\)	\(-1\)	\(+\)	\(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
1155.2.a.c	\(1\)	\(9.223\)	\(\Q\)	None	None	\(-2\)	\(1\)	\(1\)	\(1\)	\(+\)	\(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
1155.2.a.d	\(1\)	\(9.223\)	\(\Q\)	None	None	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(+\)	\(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.e	\(1\)	\(9.223\)	\(\Q\)	None	None	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(+\)	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.f	\(1\)	\(9.223\)	\(\Q\)	None	None	\(-1\)	\(1\)	\(1\)	\(1\)	\(-\)	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.g	\(1\)	\(9.223\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-1\)	\(1\)	\(+\)	\(q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
1155.2.a.h	\(1\)	\(9.223\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(+\)	\(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1155.2.a.i	\(1\)	\(9.223\)	\(\Q\)	None	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(+\)	\(q+q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
1155.2.a.j	\(1\)	\(9.223\)	\(\Q\)	None	None	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-\)	\(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.k	\(1\)	\(9.223\)	\(\Q\)	None	None	\(1\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.l	\(1\)	\(9.223\)	\(\Q\)	None	None	\(1\)	\(1\)	\(-1\)	\(-1\)	\(+\)	\(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.m	\(1\)	\(9.223\)	\(\Q\)	None	None	\(1\)	\(1\)	\(1\)	\(1\)	\(-\)	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
1155.2.a.n	\(1\)	\(9.223\)	\(\Q\)	None	None	\(2\)	\(-1\)	\(-1\)	\(-1\)	\(+\)	\(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
1155.2.a.o	\(2\)	\(9.223\)	\(\Q(\sqrt{17}) \)	None	None	\(-1\)	\(-2\)	\(2\)	\(-2\)	\(+\)	\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
1155.2.a.p	\(2\)	\(9.223\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(-2\)	\(-2\)	\(-2\)	\(-\)	\(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-q^{7}-2\beta q^{8}+\cdots\)
1155.2.a.q	\(2\)	\(9.223\)	\(\Q(\sqrt{6}) \)	None	None	\(0\)	\(2\)	\(2\)	\(2\)	\(-\)	\(q+\beta q^{2}+q^{3}+4q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots\)
1155.2.a.r	\(2\)	\(9.223\)	\(\Q(\sqrt{3}) \)	None	None	\(2\)	\(-2\)	\(-2\)	\(2\)	\(-\)	\(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots\)
1155.2.a.s	\(3\)	\(9.223\)	3.3.316.1	None	None	\(1\)	\(-3\)	\(3\)	\(-3\)	\(-\)	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1155.2.a.t	\(3\)	\(9.223\)	3.3.316.1	None	None	\(1\)	\(3\)	\(3\)	\(-3\)	\(-\)	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1155.2.a.u	\(4\)	\(9.223\)	4.4.13448.1	None	None	\(0\)	\(4\)	\(-4\)	\(-4\)	\(-\)	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
1155.2.a.v	\(4\)	\(9.223\)	4.4.7232.1	None	None	\(2\)	\(-4\)	\(4\)	\(4\)	\(-\)	\(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
1155.2.a.w	\(5\)	\(9.223\)	5.5.352076.1	None	None	\(1\)	\(5\)	\(-5\)	\(5\)	\(-\)	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
1155.2.c.a	\(2\)	\(9.223\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+iq^{2}+iq^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
1155.2.c.b	\(2\)	\(9.223\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+iq^{2}+iq^{3}+q^{4}+(-2-i)q^{5}+\cdots\)
1155.2.c.c	\(6\)	\(9.223\)	6.0.350464.1	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1155.2.c.d	\(6\)	\(9.223\)	6.0.350464.1	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1155.2.c.e	\(20\)	\(9.223\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+\beta _{1}q^{2}+\beta _{13}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
1155.2.c.f	\(20\)	\(9.223\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
1155.2.i.a	\(8\)	\(9.223\)	8.0.303595776.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{1}-\beta _{5})q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+\cdots\)
1155.2.i.b	\(8\)	\(9.223\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{24}^{4}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
1155.2.i.c	\(16\)	\(9.223\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{8}q^{2}+\beta _{9}q^{3}+(-2-\beta _{3})q^{4}-\beta _{9}q^{5}+\cdots\)
1155.2.i.d	\(32\)	\(9.223\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
1155.2.k.a	\(48\)	\(9.223\)		None	None	\(0\)	\(-48\)	\(4\)	\(0\)
1155.2.k.b	\(48\)	\(9.223\)		None	None	\(0\)	\(48\)	\(-4\)	\(0\)
1155.2.l.a	\(4\)	\(9.223\)	\(\Q(\zeta_{8})\)	None	None	\(-4\)	\(4\)	\(0\)	\(0\)		\(q+(-1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
1155.2.l.b	\(4\)	\(9.223\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(4\)	\(0\)	\(0\)		\(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
1155.2.l.c	\(4\)	\(9.223\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(4\)	\(0\)	\(0\)		\(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
1155.2.l.d	\(4\)	\(9.223\)	\(\Q(\zeta_{8})\)	None	None	\(4\)	\(4\)	\(0\)	\(0\)		\(q+(1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8}^{3})q^{4}+\cdots\)
1155.2.l.e	\(40\)	\(9.223\)		None	None	\(-4\)	\(-4\)	\(0\)	\(0\)
1155.2.l.f	\(40\)	\(9.223\)		None	None	\(4\)	\(-4\)	\(0\)	\(0\)
1155.2.q.a	\(2\)	\(9.223\)	\(\Q(\sqrt{-3}) \)	None	None	\(-2\)	\(-1\)	\(-1\)	\(-1\)		\(q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
1155.2.q.b	\(2\)	\(9.223\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-1\)	\(-5\)		\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
1155.2.q.c	\(2\)	\(9.223\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-1\)	\(5\)		\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)

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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.