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
		Only for weight 1:
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Results (displaying matches 1-50 of at least 1000) 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
8001.2.a.a	$1$	$63.888$	$\Q$	None	$-2$	$0$	$-3$	$-1$	$-$	$q-2q^{2}+2q^{4}-3q^{5}-q^{7}+6q^{10}+\cdots$
8001.2.a.b	$1$	$63.888$	$\Q$	None	$-2$	$0$	$-1$	$-1$	$-$	$q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots$
8001.2.a.c	$1$	$63.888$	$\Q$	None	$0$	$0$	$-3$	$1$	$-$	$q-2q^{4}-3q^{5}+q^{7}-6q^{11}-q^{13}+\cdots$
8001.2.a.d	$1$	$63.888$	$\Q$	None	$1$	$0$	$-4$	$-1$	$+$	$q+q^{2}-q^{4}-4q^{5}-q^{7}-3q^{8}-4q^{10}+\cdots$
8001.2.a.e	$1$	$63.888$	$\Q$	None	$1$	$0$	$0$	$1$	$+$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+2q^{13}+q^{14}+\cdots$
8001.2.a.f	$1$	$63.888$	$\Q$	None	$2$	$0$	$0$	$-1$	$+$	$q+2q^{2}+2q^{4}-q^{7}+2q^{13}-2q^{14}+\cdots$
8001.2.a.g	$1$	$63.888$	$\Q$	None	$2$	$0$	$1$	$-1$	$-$	$q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots$
8001.2.a.h	$2$	$63.888$	$\Q(\sqrt{17}) $	None	$-1$	$0$	$-3$	$-2$	$+$	$q-\beta q^{2}+(2+\beta )q^{4}+(-1-\beta )q^{5}-q^{7}+\cdots$
8001.2.a.i	$2$	$63.888$	$\Q(\sqrt{17}) $	None	$0$	$0$	$3$	$-2$	$+$	$q-2q^{4}+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+\cdots$
8001.2.a.j	$2$	$63.888$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$2$	$+$	$q+\beta q^{2}-\beta q^{5}+q^{7}-2\beta q^{8}-2q^{10}+\cdots$
8001.2.a.k	$2$	$63.888$	$\Q(\sqrt{6}) $	None	$0$	$0$	$0$	$2$	$-$	$q+\beta q^{2}+4q^{4}+\beta q^{5}+q^{7}+2\beta q^{8}+\cdots$
8001.2.a.l	$7$	$63.888$	7.7.118870813.1	None	$2$	$0$	$8$	$7$	$+$	$q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
8001.2.a.m	$11$	$63.888$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	$2$	$0$	$-1$	$-11$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}-q^{7}+\cdots$
8001.2.a.n	$12$	$63.888$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$7$	$0$	$7$	$12$	$-$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{6}+\beta _{7})q^{4}+\cdots$
8001.2.a.o	$13$	$63.888$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	$-4$	$0$	$-12$	$13$	$+$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{10}+\cdots)q^{5}+\cdots$
8001.2.a.p	$14$	$63.888$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$5$	$0$	$4$	$-14$	$-$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}-q^{7}+\cdots$
8001.2.a.q	$15$	$63.888$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	$0$	$0$	$-7$	$-15$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}-q^{7}+\cdots$
8001.2.a.r	$16$	$63.888$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-5$	$0$	$1$	$-16$	$+$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}-q^{7}+\cdots$
8001.2.a.s	$16$	$63.888$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-4$	$0$	$-5$	$-16$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}-q^{7}+\cdots$
8001.2.a.t	$16$	$63.888$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$2$	$0$	$9$	$-16$	$-$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{11})q^{5}+\cdots$
8001.2.a.u	$18$	$63.888$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$6$	$0$	$10$	$18$	$-$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{12})q^{5}+\cdots$
8001.2.a.v	$19$	$63.888$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	$-4$	$0$	$-5$	$19$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+q^{7}+\cdots$
8001.2.a.w	$20$	$63.888$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$-8$	$0$	$-3$	$20$	$+$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{16}q^{5}+q^{7}+\cdots$
8001.2.a.x	$22$	$63.888$		None	$0$	$0$	$0$	$22$	$+$
8001.2.a.y	$28$	$63.888$		None	$0$	$0$	$0$	$-28$	$-$
8001.2.a.z	$32$	$63.888$		None	$0$	$0$	$0$	$-32$	$+$
8001.2.a.ba	$40$	$63.888$		None	$0$	$0$	$0$	$40$	$-$
8002.2.a.a	$1$	$63.896$	$\Q$	None	$1$	$-1$	$1$	$0$	$+$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
8002.2.a.b	$1$	$63.896$	$\Q$	None	$1$	$0$	$0$	$0$	$+$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots$
8002.2.a.c	$1$	$63.896$	$\Q$	None	$1$	$2$	$-2$	$0$	$+$	$q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots$
8002.2.a.d	$69$	$63.896$		None	$69$	$-25$	$-33$	$-19$	$+$
8002.2.a.e	$77$	$63.896$		None	$-77$	$10$	$18$	$21$	$-$
8002.2.a.f	$89$	$63.896$		None	$-89$	$-12$	$-18$	$-27$	$+$
8002.2.a.g	$95$	$63.896$		None	$95$	$24$	$36$	$21$	$-$
8003.2.a.a	$147$	$63.904$		None	$-6$	$-23$	$-25$	$-33$	$+$
8003.2.a.b	$153$	$63.904$		None	$-9$	$-17$	$-31$	$-17$	$+$
8003.2.a.c	$172$	$63.904$		None	$8$	$25$	$27$	$31$	$-$
8003.2.a.d	$179$	$63.904$		None	$8$	$15$	$27$	$23$	$-$
8004.2.a.a	$1$	$63.912$	$\Q$	None	$0$	$-1$	$-2$	$-5$	$+$	$q-q^{3}-2q^{5}-5q^{7}+q^{9}-3q^{11}+\cdots$
8004.2.a.b	$1$	$63.912$	$\Q$	None	$0$	$-1$	$-2$	$2$	$-$	$q-q^{3}-2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
8004.2.a.c	$1$	$63.912$	$\Q$	None	$0$	$1$	$-2$	$3$	$+$	$q+q^{3}-2q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots$
8004.2.a.d	$8$	$63.912$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$8$	$-5$	$-4$	$+$	$q+q^{3}+(-1-\beta _{7})q^{5}+(\beta _{6}+\beta _{7})q^{7}+\cdots$
8004.2.a.e	$9$	$63.912$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$-9$	$-3$	$7$	$+$	$q-q^{3}+\beta _{1}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots$
8004.2.a.f	$9$	$63.912$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$9$	$-1$	$-5$	$+$	$q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+q^{9}+\cdots$
8004.2.a.g	$12$	$63.912$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$-12$	$-3$	$4$	$+$	$q-q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots$
8004.2.a.h	$13$	$63.912$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	$0$	$-13$	$5$	$-8$	$-$	$q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{12})q^{7}+q^{9}+\cdots$
8004.2.a.i	$16$	$63.912$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$-16$	$5$	$-4$	$-$	$q-q^{3}+\beta _{1}q^{5}-\beta _{12}q^{7}+q^{9}-\beta _{4}q^{11}+\cdots$
8004.2.a.j	$16$	$63.912$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$16$	$3$	$4$	$-$	$q+q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+q^{9}-\beta _{6}q^{11}+\cdots$
8004.2.a.k	$18$	$63.912$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$0$	$18$	$5$	$6$	$-$	$q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}-\beta _{9}q^{11}+\cdots$
8005.2.a.a	$1$	$63.920$	$\Q$	None	$-1$	$-2$	$1$	$2$	$+$	$q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots$

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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
8001.2.a.a	\(1\)	\(63.888\)	\(\Q\)	None	\(-2\)	\(0\)	\(-3\)	\(-1\)	\(-\)	\(q-2q^{2}+2q^{4}-3q^{5}-q^{7}+6q^{10}+\cdots\)
8001.2.a.b	\(1\)	\(63.888\)	\(\Q\)	None	\(-2\)	\(0\)	\(-1\)	\(-1\)	\(-\)	\(q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots\)
8001.2.a.c	\(1\)	\(63.888\)	\(\Q\)	None	\(0\)	\(0\)	\(-3\)	\(1\)	\(-\)	\(q-2q^{4}-3q^{5}+q^{7}-6q^{11}-q^{13}+\cdots\)
8001.2.a.d	\(1\)	\(63.888\)	\(\Q\)	None	\(1\)	\(0\)	\(-4\)	\(-1\)	\(+\)	\(q+q^{2}-q^{4}-4q^{5}-q^{7}-3q^{8}-4q^{10}+\cdots\)
8001.2.a.e	\(1\)	\(63.888\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(q+q^{2}-q^{4}+q^{7}-3q^{8}+2q^{13}+q^{14}+\cdots\)
8001.2.a.f	\(1\)	\(63.888\)	\(\Q\)	None	\(2\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(q+2q^{2}+2q^{4}-q^{7}+2q^{13}-2q^{14}+\cdots\)
8001.2.a.g	\(1\)	\(63.888\)	\(\Q\)	None	\(2\)	\(0\)	\(1\)	\(-1\)	\(-\)	\(q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots\)
8001.2.a.h	\(2\)	\(63.888\)	\(\Q(\sqrt{17}) \)	None	\(-1\)	\(0\)	\(-3\)	\(-2\)	\(+\)	\(q-\beta q^{2}+(2+\beta )q^{4}+(-1-\beta )q^{5}-q^{7}+\cdots\)
8001.2.a.i	\(2\)	\(63.888\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(0\)	\(3\)	\(-2\)	\(+\)	\(q-2q^{4}+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+\cdots\)
8001.2.a.j	\(2\)	\(63.888\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(2\)	\(+\)	\(q+\beta q^{2}-\beta q^{5}+q^{7}-2\beta q^{8}-2q^{10}+\cdots\)
8001.2.a.k	\(2\)	\(63.888\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(0\)	\(0\)	\(2\)	\(-\)	\(q+\beta q^{2}+4q^{4}+\beta q^{5}+q^{7}+2\beta q^{8}+\cdots\)
8001.2.a.l	\(7\)	\(63.888\)	7.7.118870813.1	None	\(2\)	\(0\)	\(8\)	\(7\)	\(+\)	\(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
8001.2.a.m	\(11\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	\(2\)	\(0\)	\(-1\)	\(-11\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}-q^{7}+\cdots\)
8001.2.a.n	\(12\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(7\)	\(0\)	\(7\)	\(12\)	\(-\)	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
8001.2.a.o	\(13\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	\(-4\)	\(0\)	\(-12\)	\(13\)	\(+\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{10}+\cdots)q^{5}+\cdots\)
8001.2.a.p	\(14\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(5\)	\(0\)	\(4\)	\(-14\)	\(-\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}-q^{7}+\cdots\)
8001.2.a.q	\(15\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	\(0\)	\(0\)	\(-7\)	\(-15\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}-q^{7}+\cdots\)
8001.2.a.r	\(16\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-5\)	\(0\)	\(1\)	\(-16\)	\(+\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}-q^{7}+\cdots\)
8001.2.a.s	\(16\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-4\)	\(0\)	\(-5\)	\(-16\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}-q^{7}+\cdots\)
8001.2.a.t	\(16\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(2\)	\(0\)	\(9\)	\(-16\)	\(-\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{11})q^{5}+\cdots\)
8001.2.a.u	\(18\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(6\)	\(0\)	\(10\)	\(18\)	\(-\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{12})q^{5}+\cdots\)
8001.2.a.v	\(19\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	\(-4\)	\(0\)	\(-5\)	\(19\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+q^{7}+\cdots\)
8001.2.a.w	\(20\)	\(63.888\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(-8\)	\(0\)	\(-3\)	\(20\)	\(+\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{16}q^{5}+q^{7}+\cdots\)
8001.2.a.x	\(22\)	\(63.888\)		None	\(0\)	\(0\)	\(0\)	\(22\)	\(+\)
8001.2.a.y	\(28\)	\(63.888\)		None	\(0\)	\(0\)	\(0\)	\(-28\)	\(-\)
8001.2.a.z	\(32\)	\(63.888\)		None	\(0\)	\(0\)	\(0\)	\(-32\)	\(+\)
8001.2.a.ba	\(40\)	\(63.888\)		None	\(0\)	\(0\)	\(0\)	\(40\)	\(-\)
8002.2.a.a	\(1\)	\(63.896\)	\(\Q\)	None	\(1\)	\(-1\)	\(1\)	\(0\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
8002.2.a.b	\(1\)	\(63.896\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots\)
8002.2.a.c	\(1\)	\(63.896\)	\(\Q\)	None	\(1\)	\(2\)	\(-2\)	\(0\)	\(+\)	\(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots\)
8002.2.a.d	\(69\)	\(63.896\)		None	\(69\)	\(-25\)	\(-33\)	\(-19\)	\(+\)
8002.2.a.e	\(77\)	\(63.896\)		None	\(-77\)	\(10\)	\(18\)	\(21\)	\(-\)
8002.2.a.f	\(89\)	\(63.896\)		None	\(-89\)	\(-12\)	\(-18\)	\(-27\)	\(+\)
8002.2.a.g	\(95\)	\(63.896\)		None	\(95\)	\(24\)	\(36\)	\(21\)	\(-\)
8003.2.a.a	\(147\)	\(63.904\)		None	\(-6\)	\(-23\)	\(-25\)	\(-33\)	\(+\)
8003.2.a.b	\(153\)	\(63.904\)		None	\(-9\)	\(-17\)	\(-31\)	\(-17\)	\(+\)
8003.2.a.c	\(172\)	\(63.904\)		None	\(8\)	\(25\)	\(27\)	\(31\)	\(-\)
8003.2.a.d	\(179\)	\(63.904\)		None	\(8\)	\(15\)	\(27\)	\(23\)	\(-\)
8004.2.a.a	\(1\)	\(63.912\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(-5\)	\(+\)	\(q-q^{3}-2q^{5}-5q^{7}+q^{9}-3q^{11}+\cdots\)
8004.2.a.b	\(1\)	\(63.912\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(2\)	\(-\)	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
8004.2.a.c	\(1\)	\(63.912\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(3\)	\(+\)	\(q+q^{3}-2q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
8004.2.a.d	\(8\)	\(63.912\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(8\)	\(-5\)	\(-4\)	\(+\)	\(q+q^{3}+(-1-\beta _{7})q^{5}+(\beta _{6}+\beta _{7})q^{7}+\cdots\)
8004.2.a.e	\(9\)	\(63.912\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(-9\)	\(-3\)	\(7\)	\(+\)	\(q-q^{3}+\beta _{1}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
8004.2.a.f	\(9\)	\(63.912\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(9\)	\(-1\)	\(-5\)	\(+\)	\(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+q^{9}+\cdots\)
8004.2.a.g	\(12\)	\(63.912\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(-12\)	\(-3\)	\(4\)	\(+\)	\(q-q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
8004.2.a.h	\(13\)	\(63.912\)	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	\(0\)	\(-13\)	\(5\)	\(-8\)	\(-\)	\(q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{12})q^{7}+q^{9}+\cdots\)
8004.2.a.i	\(16\)	\(63.912\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(-16\)	\(5\)	\(-4\)	\(-\)	\(q-q^{3}+\beta _{1}q^{5}-\beta _{12}q^{7}+q^{9}-\beta _{4}q^{11}+\cdots\)
8004.2.a.j	\(16\)	\(63.912\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(16\)	\(3\)	\(4\)	\(-\)	\(q+q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+q^{9}-\beta _{6}q^{11}+\cdots\)
8004.2.a.k	\(18\)	\(63.912\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(0\)	\(18\)	\(5\)	\(6\)	\(-\)	\(q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}-\beta _{9}q^{11}+\cdots\)
8005.2.a.a	\(1\)	\(63.920\)	\(\Q\)	None	\(-1\)	\(-2\)	\(1\)	\(2\)	\(+\)	\(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)

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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.