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 231 matches)

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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
49.2.a.a	$1$	$0.391$	$\Q$	$\Q(\sqrt{-7}) $	$1$	$0$	$0$	$0$	$-$	$q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots$
49.2.c.a	$2$	$0.391$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $	$-1$	$0$	$0$	$0$		$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots$
49.2.e.a	$6$	$0.391$	$\Q(\zeta_{14})$	None	$-3$	$-3$	$6$	$7$		$q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
49.2.e.b	$12$	$0.391$	$\Q(\zeta_{21})$	None	$-2$	$0$	$-7$	$-7$		$q+(\zeta_{21}^{2}+\zeta_{21}^{4}-\zeta_{21}^{5}-\zeta_{21}^{9}+\zeta_{21}^{11})q^{2}+\cdots$
49.2.g.a	$48$	$0.391$		None	$-13$	$-14$	$-14$	$-14$
49.3.b.a	$4$	$1.335$	4.0.2048.2	None	$4$	$0$	$0$	$0$		$q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots$
49.3.d.a	$2$	$1.335$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $	$3$	$0$	$0$	$0$		$q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}-3q^{8}+\cdots$
49.3.d.b	$8$	$1.335$	8.0.339738624.1	None	$-4$	$0$	$0$	$0$		$q+(\beta _{4}-\beta _{5})q^{2}+\beta _{1}q^{3}+(1+2\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
49.3.f.a	$54$	$1.335$		None	$-5$	$-7$	$-7$	$0$
49.3.h.a	$96$	$1.335$		None	$-13$	$-14$	$-14$	$-14$
49.4.a.a	$1$	$2.891$	$\Q$	$\Q(\sqrt{-7}) $	$-5$	$0$	$0$	$0$	$-$	$q-5q^{2}+17q^{4}-45q^{8}-3^{3}q^{9}-68q^{11}+\cdots$
49.4.a.b	$1$	$2.891$	$\Q$	None	$-1$	$2$	$-16$	$0$	$-$	$q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots$
49.4.a.c	$1$	$2.891$	$\Q$	None	$2$	$-7$	$-7$	$0$	$-$	$q+2q^{2}-7q^{3}-4q^{4}-7q^{5}-14q^{6}+\cdots$
49.4.a.d	$1$	$2.891$	$\Q$	None	$2$	$7$	$7$	$0$	$+$	$q+2q^{2}+7q^{3}-4q^{4}+7q^{5}+14q^{6}+\cdots$
49.4.a.e	$4$	$2.891$	$\Q(\sqrt{2}, \sqrt{65})$	None	$2$	$0$	$0$	$0$	$+$	$q+(1+\beta _{1})q^{2}+\beta _{2}q^{3}+(9+\beta _{1})q^{4}+\cdots$
49.4.c.a	$2$	$2.891$	$\Q(\sqrt{-3}) $	None	$-2$	$7$	$7$	$0$		$q-2\zeta_{6}q^{2}+(7-7\zeta_{6})q^{3}+(4-4\zeta_{6})q^{4}+\cdots$
49.4.c.b	$2$	$2.891$	$\Q(\sqrt{-3}) $	None	$1$	$-2$	$16$	$0$		$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots$
49.4.c.c	$2$	$2.891$	$\Q(\sqrt{-3}) $	None	$1$	$2$	$-16$	$0$		$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots$
49.4.c.d	$2$	$2.891$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $	$5$	$0$	$0$	$0$		$q+5\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-45q^{8}+\cdots$
49.4.c.e	$8$	$2.891$	8.0.$\cdots$.19	None	$-2$	$0$	$0$	$0$		$q+(-1+\beta _{2}-\beta _{6})q^{2}+\beta _{3}q^{3}+(-8+\cdots)q^{4}+\cdots$
49.4.e.a	$78$	$2.891$		None	$-5$	$-5$	$-23$	$0$
49.4.g.a	$156$	$2.891$		None	$-13$	$-7$	$-7$	$-42$
49.5.b.a	$4$	$5.065$	$\Q(\sqrt{-3}, \sqrt{22})$	None	$8$	$0$	$0$	$0$		$q+(2+\beta _{1})q^{2}+\beta _{2}q^{3}+(10+4\beta _{1})q^{4}+\cdots$
49.5.b.b	$8$	$5.065$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-12$	$0$	$0$	$0$		$q+(-2-\beta _{2})q^{2}-\beta _{3}q^{3}+(8+\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots$
49.5.d.a	$2$	$5.065$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $	$-1$	$0$	$0$	$0$		$q-\zeta_{6}q^{2}+(15-15\zeta_{6})q^{4}-31q^{8}+\cdots$
49.5.d.b	$4$	$5.065$	$\Q(\sqrt{-3}, \sqrt{22})$	None	$-4$	$-6$	$30$	$0$		$q+(-2+\beta _{1}-2\beta _{2})q^{2}+(-2+\beta _{1}+\cdots)q^{3}+\cdots$
49.5.d.c	$16$	$5.065$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$12$	$0$	$0$	$0$		$q+(1+\beta _{2}+\beta _{12})q^{2}+\beta _{5}q^{3}+(5\beta _{2}+\cdots)q^{4}+\cdots$
49.5.f.a	$102$	$5.065$		None	$-5$	$-7$	$-7$	$-56$
49.5.h.a	$216$	$5.065$		None	$-13$	$-20$	$16$	$-14$
49.6.a.a	$1$	$7.859$	$\Q$	None	$-10$	$14$	$56$	$0$	$-$	$q-10q^{2}+14q^{3}+68q^{4}+56q^{5}+\cdots$
49.6.a.b	$1$	$7.859$	$\Q$	$\Q(\sqrt{-7}) $	$11$	$0$	$0$	$0$	$-$	$q+11q^{2}+89q^{4}+627q^{8}-3^{5}q^{9}+\cdots$
49.6.a.c	$2$	$7.859$	$\Q(\sqrt{39}) $	None	$-4$	$0$	$0$	$0$	$-$	$q-2q^{2}+\beta q^{3}-28q^{4}+3\beta q^{5}-2\beta q^{6}+\cdots$
49.6.a.d	$2$	$7.859$	$\Q(\sqrt{37}) $	None	$2$	$-8$	$-38$	$0$	$+$	$q+(1+\beta )q^{2}+(-4-\beta )q^{3}+(6+2\beta )q^{4}+\cdots$
49.6.a.e	$2$	$7.859$	$\Q(\sqrt{37}) $	None	$2$	$8$	$38$	$0$	$-$	$q+(1+\beta )q^{2}+(4+\beta )q^{3}+(6+2\beta )q^{4}+\cdots$
49.6.a.f	$2$	$7.859$	$\Q(\sqrt{57}) $	None	$9$	$6$	$18$	$0$	$-$	$q+(5-\beta )q^{2}+(6-6\beta )q^{3}+(7-9\beta )q^{4}+\cdots$
49.6.a.g	$4$	$7.859$	$\Q(\sqrt{2}, \sqrt{113})$	None	$-10$	$0$	$0$	$0$	$+$	$q+(-2+\beta _{1})q^{2}+(2\beta _{2}-\beta _{3})q^{3}-5\beta _{1}q^{4}+\cdots$
49.6.c.a	$2$	$7.859$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $	$-11$	$0$	$0$	$0$		$q-11\zeta_{6}q^{2}+(-89+89\zeta_{6})q^{4}+627q^{8}+\cdots$
49.6.c.b	$2$	$7.859$	$\Q(\sqrt{-3}) $	None	$10$	$-14$	$-56$	$0$		$q+10\zeta_{6}q^{2}+(-14+14\zeta_{6})q^{3}+(-68+\cdots)q^{4}+\cdots$
49.6.c.c	$2$	$7.859$	$\Q(\sqrt{-3}) $	None	$10$	$14$	$56$	$0$		$q+10\zeta_{6}q^{2}+(14-14\zeta_{6})q^{3}+(-68+\cdots)q^{4}+\cdots$
49.6.c.d	$4$	$7.859$	$\Q(\sqrt{-3}, \sqrt{-19})$	None	$-9$	$-6$	$-18$	$0$		$q+(5\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(-6-6\beta _{1}+\cdots)q^{3}+\cdots$
49.6.c.e	$4$	$7.859$	$\Q(\sqrt{-3}, \sqrt{-19})$	None	$-9$	$6$	$18$	$0$		$q+(5\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(6+6\beta _{1}-6\beta _{3})q^{3}+\cdots$
49.6.c.f	$4$	$7.859$	$\Q(\sqrt{-3}, \sqrt{37})$	None	$-2$	$-8$	$-38$	$0$		$q+(-\beta _{1}-\beta _{2})q^{2}+(-4+4\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
49.6.c.g	$4$	$7.859$	$\Q(\sqrt{-3}, \sqrt{-13})$	None	$4$	$0$	$0$	$0$		$q+(2-2\beta _{1})q^{2}+\beta _{2}q^{3}+28\beta _{1}q^{4}+\cdots$
49.6.c.h	$8$	$7.859$	8.0.$\cdots$.19	None	$10$	$0$	$0$	$0$		$q+(3-2\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{3}+\cdots$
49.6.e.a	$138$	$7.859$		None	$-5$	$13$	$67$	$-56$
49.6.g.a	$264$	$7.859$		None	$-13$	$-22$	$-52$	$154$
49.7.b.a	$2$	$11.273$	$\Q(\sqrt{-3}) $	None	$-24$	$0$	$0$	$0$		$q-12q^{2}-\zeta_{6}q^{3}+80q^{4}-15\zeta_{6}q^{5}+\cdots$
49.7.b.b	$4$	$11.273$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$16$	$0$	$0$	$0$		$q+(4+\beta _{1})q^{2}+(6\beta _{2}-\beta _{3})q^{3}+(-30+\cdots)q^{4}+\cdots$
49.7.b.c	$12$	$11.273$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$20$	$0$	$0$	$0$		$q+(2-\beta _{1})q^{2}+\beta _{3}q^{3}+(47-\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots$
49.7.d.a	$2$	$11.273$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $	$-9$	$0$	$0$	$0$		$q-9\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-423q^{8}+\cdots$

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$\zeta$ zeros

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Elliptic curves over $\Q$
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Higher genus families
Abelian varieties over $\F_{q}$

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
49.2.a.a	\(1\)	\(0.391\)	\(\Q\)	\(\Q(\sqrt{-7}) \)	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots\)
49.2.c.a	\(2\)	\(0.391\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \)	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots\)
49.2.e.a	\(6\)	\(0.391\)	\(\Q(\zeta_{14})\)	None	\(-3\)	\(-3\)	\(6\)	\(7\)		\(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
49.2.e.b	\(12\)	\(0.391\)	\(\Q(\zeta_{21})\)	None	\(-2\)	\(0\)	\(-7\)	\(-7\)		\(q+(\zeta_{21}^{2}+\zeta_{21}^{4}-\zeta_{21}^{5}-\zeta_{21}^{9}+\zeta_{21}^{11})q^{2}+\cdots\)
49.2.g.a	\(48\)	\(0.391\)		None	\(-13\)	\(-14\)	\(-14\)	\(-14\)
49.3.b.a	\(4\)	\(1.335\)	4.0.2048.2	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots\)
49.3.d.a	\(2\)	\(1.335\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \)	\(3\)	\(0\)	\(0\)	\(0\)		\(q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}-3q^{8}+\cdots\)
49.3.d.b	\(8\)	\(1.335\)	8.0.339738624.1	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{4}-\beta _{5})q^{2}+\beta _{1}q^{3}+(1+2\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
49.3.f.a	\(54\)	\(1.335\)		None	\(-5\)	\(-7\)	\(-7\)	\(0\)
49.3.h.a	\(96\)	\(1.335\)		None	\(-13\)	\(-14\)	\(-14\)	\(-14\)
49.4.a.a	\(1\)	\(2.891\)	\(\Q\)	\(\Q(\sqrt{-7}) \)	\(-5\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q-5q^{2}+17q^{4}-45q^{8}-3^{3}q^{9}-68q^{11}+\cdots\)
49.4.a.b	\(1\)	\(2.891\)	\(\Q\)	None	\(-1\)	\(2\)	\(-16\)	\(0\)	\(-\)	\(q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots\)
49.4.a.c	\(1\)	\(2.891\)	\(\Q\)	None	\(2\)	\(-7\)	\(-7\)	\(0\)	\(-\)	\(q+2q^{2}-7q^{3}-4q^{4}-7q^{5}-14q^{6}+\cdots\)
49.4.a.d	\(1\)	\(2.891\)	\(\Q\)	None	\(2\)	\(7\)	\(7\)	\(0\)	\(+\)	\(q+2q^{2}+7q^{3}-4q^{4}+7q^{5}+14q^{6}+\cdots\)
49.4.a.e	\(4\)	\(2.891\)	\(\Q(\sqrt{2}, \sqrt{65})\)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q+(1+\beta _{1})q^{2}+\beta _{2}q^{3}+(9+\beta _{1})q^{4}+\cdots\)
49.4.c.a	\(2\)	\(2.891\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(7\)	\(7\)	\(0\)		\(q-2\zeta_{6}q^{2}+(7-7\zeta_{6})q^{3}+(4-4\zeta_{6})q^{4}+\cdots\)
49.4.c.b	\(2\)	\(2.891\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-2\)	\(16\)	\(0\)		\(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
49.4.c.c	\(2\)	\(2.891\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(2\)	\(-16\)	\(0\)		\(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
49.4.c.d	\(2\)	\(2.891\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \)	\(5\)	\(0\)	\(0\)	\(0\)		\(q+5\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-45q^{8}+\cdots\)
49.4.c.e	\(8\)	\(2.891\)	8.0.\(\cdots\).19	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+(-1+\beta _{2}-\beta _{6})q^{2}+\beta _{3}q^{3}+(-8+\cdots)q^{4}+\cdots\)
49.4.e.a	\(78\)	\(2.891\)		None	\(-5\)	\(-5\)	\(-23\)	\(0\)
49.4.g.a	\(156\)	\(2.891\)		None	\(-13\)	\(-7\)	\(-7\)	\(-42\)
49.5.b.a	\(4\)	\(5.065\)	\(\Q(\sqrt{-3}, \sqrt{22})\)	None	\(8\)	\(0\)	\(0\)	\(0\)		\(q+(2+\beta _{1})q^{2}+\beta _{2}q^{3}+(10+4\beta _{1})q^{4}+\cdots\)
49.5.b.b	\(8\)	\(5.065\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-12\)	\(0\)	\(0\)	\(0\)		\(q+(-2-\beta _{2})q^{2}-\beta _{3}q^{3}+(8+\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots\)
49.5.d.a	\(2\)	\(5.065\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \)	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{6}q^{2}+(15-15\zeta_{6})q^{4}-31q^{8}+\cdots\)
49.5.d.b	\(4\)	\(5.065\)	\(\Q(\sqrt{-3}, \sqrt{22})\)	None	\(-4\)	\(-6\)	\(30\)	\(0\)		\(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(-2+\beta _{1}+\cdots)q^{3}+\cdots\)
49.5.d.c	\(16\)	\(5.065\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(12\)	\(0\)	\(0\)	\(0\)		\(q+(1+\beta _{2}+\beta _{12})q^{2}+\beta _{5}q^{3}+(5\beta _{2}+\cdots)q^{4}+\cdots\)
49.5.f.a	\(102\)	\(5.065\)		None	\(-5\)	\(-7\)	\(-7\)	\(-56\)
49.5.h.a	\(216\)	\(5.065\)		None	\(-13\)	\(-20\)	\(16\)	\(-14\)
49.6.a.a	\(1\)	\(7.859\)	\(\Q\)	None	\(-10\)	\(14\)	\(56\)	\(0\)	\(-\)	\(q-10q^{2}+14q^{3}+68q^{4}+56q^{5}+\cdots\)
49.6.a.b	\(1\)	\(7.859\)	\(\Q\)	\(\Q(\sqrt{-7}) \)	\(11\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+11q^{2}+89q^{4}+627q^{8}-3^{5}q^{9}+\cdots\)
49.6.a.c	\(2\)	\(7.859\)	\(\Q(\sqrt{39}) \)	None	\(-4\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q-2q^{2}+\beta q^{3}-28q^{4}+3\beta q^{5}-2\beta q^{6}+\cdots\)
49.6.a.d	\(2\)	\(7.859\)	\(\Q(\sqrt{37}) \)	None	\(2\)	\(-8\)	\(-38\)	\(0\)	\(+\)	\(q+(1+\beta )q^{2}+(-4-\beta )q^{3}+(6+2\beta )q^{4}+\cdots\)
49.6.a.e	\(2\)	\(7.859\)	\(\Q(\sqrt{37}) \)	None	\(2\)	\(8\)	\(38\)	\(0\)	\(-\)	\(q+(1+\beta )q^{2}+(4+\beta )q^{3}+(6+2\beta )q^{4}+\cdots\)
49.6.a.f	\(2\)	\(7.859\)	\(\Q(\sqrt{57}) \)	None	\(9\)	\(6\)	\(18\)	\(0\)	\(-\)	\(q+(5-\beta )q^{2}+(6-6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\)
49.6.a.g	\(4\)	\(7.859\)	\(\Q(\sqrt{2}, \sqrt{113})\)	None	\(-10\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q+(-2+\beta _{1})q^{2}+(2\beta _{2}-\beta _{3})q^{3}-5\beta _{1}q^{4}+\cdots\)
49.6.c.a	\(2\)	\(7.859\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \)	\(-11\)	\(0\)	\(0\)	\(0\)		\(q-11\zeta_{6}q^{2}+(-89+89\zeta_{6})q^{4}+627q^{8}+\cdots\)
49.6.c.b	\(2\)	\(7.859\)	\(\Q(\sqrt{-3}) \)	None	\(10\)	\(-14\)	\(-56\)	\(0\)		\(q+10\zeta_{6}q^{2}+(-14+14\zeta_{6})q^{3}+(-68+\cdots)q^{4}+\cdots\)
49.6.c.c	\(2\)	\(7.859\)	\(\Q(\sqrt{-3}) \)	None	\(10\)	\(14\)	\(56\)	\(0\)		\(q+10\zeta_{6}q^{2}+(14-14\zeta_{6})q^{3}+(-68+\cdots)q^{4}+\cdots\)
49.6.c.d	\(4\)	\(7.859\)	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None	\(-9\)	\(-6\)	\(-18\)	\(0\)		\(q+(5\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(-6-6\beta _{1}+\cdots)q^{3}+\cdots\)
49.6.c.e	\(4\)	\(7.859\)	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None	\(-9\)	\(6\)	\(18\)	\(0\)		\(q+(5\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(6+6\beta _{1}-6\beta _{3})q^{3}+\cdots\)
49.6.c.f	\(4\)	\(7.859\)	\(\Q(\sqrt{-3}, \sqrt{37})\)	None	\(-2\)	\(-8\)	\(-38\)	\(0\)		\(q+(-\beta _{1}-\beta _{2})q^{2}+(-4+4\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
49.6.c.g	\(4\)	\(7.859\)	\(\Q(\sqrt{-3}, \sqrt{-13})\)	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+(2-2\beta _{1})q^{2}+\beta _{2}q^{3}+28\beta _{1}q^{4}+\cdots\)
49.6.c.h	\(8\)	\(7.859\)	8.0.\(\cdots\).19	None	\(10\)	\(0\)	\(0\)	\(0\)		\(q+(3-2\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{3}+\cdots\)
49.6.e.a	\(138\)	\(7.859\)		None	\(-5\)	\(13\)	\(67\)	\(-56\)
49.6.g.a	\(264\)	\(7.859\)		None	\(-13\)	\(-22\)	\(-52\)	\(154\)
49.7.b.a	\(2\)	\(11.273\)	\(\Q(\sqrt{-3}) \)	None	\(-24\)	\(0\)	\(0\)	\(0\)		\(q-12q^{2}-\zeta_{6}q^{3}+80q^{4}-15\zeta_{6}q^{5}+\cdots\)
49.7.b.b	\(4\)	\(11.273\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(16\)	\(0\)	\(0\)	\(0\)		\(q+(4+\beta _{1})q^{2}+(6\beta _{2}-\beta _{3})q^{3}+(-30+\cdots)q^{4}+\cdots\)
49.7.b.c	\(12\)	\(11.273\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(20\)	\(0\)	\(0\)	\(0\)		\(q+(2-\beta _{1})q^{2}+\beta _{3}q^{3}+(47-\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots\)
49.7.d.a	\(2\)	\(11.273\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \)	\(-9\)	\(0\)	\(0\)	\(0\)		\(q-9\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-423q^{8}+\cdots\)

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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.