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 198 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
304.1.e.a	$1$	$0.152$	$\Q$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-1$	$1$		$q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots$
304.2.a.a	$1$	$2.427$	$\Q$	None	None	$0$	$-2$	$-1$	$3$	$+$	$q-2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots$
304.2.a.b	$1$	$2.427$	$\Q$	None	None	$0$	$-1$	$0$	$-3$	$+$	$q-q^{3}-3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots$
304.2.a.c	$1$	$2.427$	$\Q$	None	None	$0$	$-1$	$0$	$1$	$-$	$q-q^{3}+q^{7}-2q^{9}+6q^{11}+5q^{13}+\cdots$
304.2.a.d	$1$	$2.427$	$\Q$	None	None	$0$	$1$	$-4$	$-3$	$+$	$q+q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
304.2.a.e	$1$	$2.427$	$\Q$	None	None	$0$	$2$	$-1$	$3$	$-$	$q+2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots$
304.2.a.f	$1$	$2.427$	$\Q$	None	None	$0$	$2$	$3$	$1$	$-$	$q+2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots$
304.2.a.g	$3$	$2.427$	3.3.961.1	None	None	$0$	$-1$	$1$	$-4$	$-$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots$
304.2.h.a	$2$	$2.427$	$\Q(\sqrt{-19}) $	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-2$	$0$		$q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots$
304.2.h.b	$4$	$2.427$	$\Q(\sqrt{-3}, \sqrt{7})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots$
304.2.h.c	$4$	$2.427$	$\Q(\sqrt{-3}, \sqrt{-19})$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$2$	$0$		$q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots$
304.2.i.a	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$1$	$0$		$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
304.2.i.b	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$-3$	$0$		$q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
304.2.i.c	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$0$	$8$		$q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots$
304.2.i.d	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$4$	$0$		$q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
304.2.i.e	$4$	$2.427$	$\Q(\sqrt{-3}, \sqrt{7})$	None	None	$0$	$0$	$-2$	$-4$		$q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
304.2.i.f	$6$	$2.427$	6.0.2696112.1	None	None	$0$	$1$	$-1$	$4$		$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
304.2.k.a	$4$	$2.427$	$\Q(\zeta_{8})$	None	None	$0$	$-4$	$-8$	$0$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$
304.2.k.b	$68$	$2.427$		None	None	$0$	$4$	$8$	$0$
304.2.m.a	$76$	$2.427$		None	None	$0$	$0$	$-4$	$-8$
304.2.n.a	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-3$	$0$		$q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots$
304.2.n.b	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$-3$	$0$		$q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$
304.2.n.c	$4$	$2.427$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$2$	$0$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots$
304.2.n.d	$6$	$2.427$	6.0.31726512.1	None	None	$0$	$-1$	$2$	$0$		$q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$
304.2.n.e	$6$	$2.427$	6.0.31726512.1	None	None	$0$	$1$	$2$	$0$		$q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots$
304.2.u.a	$6$	$2.427$	$\Q(\zeta_{18})$	None	None	$0$	$-9$	$-6$	$-6$		$q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots$
304.2.u.b	$6$	$2.427$	$\Q(\zeta_{18})$	None	None	$0$	$3$	$-6$	$0$		$q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots$
304.2.u.c	$6$	$2.427$	$\Q(\zeta_{18})$	None	None	$0$	$3$	$0$	$6$		$q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots$
304.2.u.d	$6$	$2.427$	$\Q(\zeta_{18})$	None	None	$0$	$6$	$6$	$-3$		$q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots$
304.2.u.e	$12$	$2.427$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$3$	$0$	$-3$		$q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots$
304.2.u.f	$18$	$2.427$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	None	$0$	$0$	$0$	$9$		$q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots$
304.2.v.a	$152$	$2.427$		None	None	$-2$	$-2$	$-2$	$0$
304.2.x.a	$4$	$2.427$	$\Q(\zeta_{12})$	None	None	$-2$	$2$	$-2$	$-4$		$q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
304.2.x.b	$4$	$2.427$	$\Q(\zeta_{12})$	None	None	$2$	$4$	$-2$	$-4$		$q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$
304.2.x.c	$144$	$2.427$		None	None	$-6$	$-12$	$2$	$-8$
304.2.be.a	$12$	$2.427$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots$
304.2.be.b	$12$	$2.427$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots$
304.2.be.c	$18$	$2.427$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	None	$0$	$0$	$0$	$-9$		$q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots$
304.2.be.d	$18$	$2.427$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	None	$0$	$0$	$0$	$9$		$q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots$
304.2.bg.a	$456$	$2.427$		None	None	$-12$	$-12$	$-12$	$-12$
304.2.bi.a	$456$	$2.427$		None	None	$-12$	$-12$	$-12$	$0$
304.3.d.a	$6$	$8.283$	6.0.210056875.1	None	None	$0$	$0$	$14$	$0$		$q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots$
304.3.d.b	$12$	$8.283$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$0$	$-2$	$0$		$q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots$
304.3.e.a	$1$	$8.283$	$\Q$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-9$	$5$		$q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots$
304.3.e.b	$2$	$8.283$	$\Q(\sqrt{-29}) $	None	None	$0$	$0$	$-8$	$2$		$q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots$
304.3.e.c	$2$	$8.283$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$-2$	$-10$		$q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots$
304.3.e.d	$2$	$8.283$	$\Q(\sqrt{-13}) $	None	None	$0$	$0$	$8$	$10$		$q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots$
304.3.e.e	$2$	$8.283$	$\Q(\sqrt{57}) $	$\Q(\sqrt{-19}) $	None	$0$	$0$	$9$	$-5$		$q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots$
304.3.e.f	$2$	$8.283$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$14$	$-22$		$q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots$
304.3.e.g	$8$	$8.283$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	None	$0$	$0$	$-14$	$6$		$q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots$

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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
304.1.e.a	\(1\)	\(0.152\)	\(\Q\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-1\)	\(1\)		\(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
304.2.a.a	\(1\)	\(2.427\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(-1\)	\(3\)	\(+\)	\(q-2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
304.2.a.b	\(1\)	\(2.427\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(-3\)	\(+\)	\(q-q^{3}-3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
304.2.a.c	\(1\)	\(2.427\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(1\)	\(-\)	\(q-q^{3}+q^{7}-2q^{9}+6q^{11}+5q^{13}+\cdots\)
304.2.a.d	\(1\)	\(2.427\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-4\)	\(-3\)	\(+\)	\(q+q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
304.2.a.e	\(1\)	\(2.427\)	\(\Q\)	None	None	\(0\)	\(2\)	\(-1\)	\(3\)	\(-\)	\(q+2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
304.2.a.f	\(1\)	\(2.427\)	\(\Q\)	None	None	\(0\)	\(2\)	\(3\)	\(1\)	\(-\)	\(q+2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
304.2.a.g	\(3\)	\(2.427\)	3.3.961.1	None	None	\(0\)	\(-1\)	\(1\)	\(-4\)	\(-\)	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
304.2.h.a	\(2\)	\(2.427\)	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
304.2.h.b	\(4\)	\(2.427\)	\(\Q(\sqrt{-3}, \sqrt{7})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
304.2.h.c	\(4\)	\(2.427\)	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
304.2.i.a	\(2\)	\(2.427\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(1\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.b	\(2\)	\(2.427\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(-3\)	\(0\)		\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.c	\(2\)	\(2.427\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(0\)	\(8\)		\(q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots\)
304.2.i.d	\(2\)	\(2.427\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(4\)	\(0\)		\(q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.e	\(4\)	\(2.427\)	\(\Q(\sqrt{-3}, \sqrt{7})\)	None	None	\(0\)	\(0\)	\(-2\)	\(-4\)		\(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
304.2.i.f	\(6\)	\(2.427\)	6.0.2696112.1	None	None	\(0\)	\(1\)	\(-1\)	\(4\)		\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
304.2.k.a	\(4\)	\(2.427\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(-4\)	\(-8\)	\(0\)		\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
304.2.k.b	\(68\)	\(2.427\)		None	None	\(0\)	\(4\)	\(8\)	\(0\)
304.2.m.a	\(76\)	\(2.427\)		None	None	\(0\)	\(0\)	\(-4\)	\(-8\)
304.2.n.a	\(2\)	\(2.427\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-3\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
304.2.n.b	\(2\)	\(2.427\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(-3\)	\(0\)		\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
304.2.n.c	\(4\)	\(2.427\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
304.2.n.d	\(6\)	\(2.427\)	6.0.31726512.1	None	None	\(0\)	\(-1\)	\(2\)	\(0\)		\(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
304.2.n.e	\(6\)	\(2.427\)	6.0.31726512.1	None	None	\(0\)	\(1\)	\(2\)	\(0\)		\(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
304.2.u.a	\(6\)	\(2.427\)	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(-9\)	\(-6\)	\(-6\)		\(q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
304.2.u.b	\(6\)	\(2.427\)	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(3\)	\(-6\)	\(0\)		\(q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots\)
304.2.u.c	\(6\)	\(2.427\)	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(3\)	\(0\)	\(6\)		\(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots\)
304.2.u.d	\(6\)	\(2.427\)	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(6\)	\(6\)	\(-3\)		\(q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots\)
304.2.u.e	\(12\)	\(2.427\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(3\)	\(0\)	\(-3\)		\(q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
304.2.u.f	\(18\)	\(2.427\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(9\)		\(q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
304.2.v.a	\(152\)	\(2.427\)		None	None	\(-2\)	\(-2\)	\(-2\)	\(0\)
304.2.x.a	\(4\)	\(2.427\)	\(\Q(\zeta_{12})\)	None	None	\(-2\)	\(2\)	\(-2\)	\(-4\)		\(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.b	\(4\)	\(2.427\)	\(\Q(\zeta_{12})\)	None	None	\(2\)	\(4\)	\(-2\)	\(-4\)		\(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.c	\(144\)	\(2.427\)		None	None	\(-6\)	\(-12\)	\(2\)	\(-8\)
304.2.be.a	\(12\)	\(2.427\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.b	\(12\)	\(2.427\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
304.2.be.c	\(18\)	\(2.427\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(-9\)		\(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.d	\(18\)	\(2.427\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(9\)		\(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.bg.a	\(456\)	\(2.427\)		None	None	\(-12\)	\(-12\)	\(-12\)	\(-12\)
304.2.bi.a	\(456\)	\(2.427\)		None	None	\(-12\)	\(-12\)	\(-12\)	\(0\)
304.3.d.a	\(6\)	\(8.283\)	6.0.210056875.1	None	None	\(0\)	\(0\)	\(14\)	\(0\)		\(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\)
304.3.d.b	\(12\)	\(8.283\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots\)
304.3.e.a	\(1\)	\(8.283\)	\(\Q\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-9\)	\(5\)		\(q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots\)
304.3.e.b	\(2\)	\(8.283\)	\(\Q(\sqrt{-29}) \)	None	None	\(0\)	\(0\)	\(-8\)	\(2\)		\(q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots\)
304.3.e.c	\(2\)	\(8.283\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(-10\)		\(q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots\)
304.3.e.d	\(2\)	\(8.283\)	\(\Q(\sqrt{-13}) \)	None	None	\(0\)	\(0\)	\(8\)	\(10\)		\(q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots\)
304.3.e.e	\(2\)	\(8.283\)	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(9\)	\(-5\)		\(q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots\)
304.3.e.f	\(2\)	\(8.283\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(14\)	\(-22\)		\(q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots\)
304.3.e.g	\(8\)	\(8.283\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	None	\(0\)	\(0\)	\(-14\)	\(6\)		\(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots\)

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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.