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 135 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
190.2.a.a	$1$	$1.517$	$\Q$	None	$-1$	$-1$	$-1$	$-1$	$+$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
190.2.a.b	$1$	$1.517$	$\Q$	None	$1$	$-3$	$-1$	$-5$	$+$	$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots$
190.2.a.c	$1$	$1.517$	$\Q$	None	$1$	$1$	$1$	$-1$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
190.2.a.d	$2$	$1.517$	$\Q(\sqrt{17}) $	None	$-2$	$-1$	$2$	$-1$	$-$	$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots$
190.2.b.a	$4$	$1.517$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
190.2.b.b	$6$	$1.517$	6.0.5161984.1	None	$0$	$0$	$2$	$0$		$q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
190.2.e.a	$2$	$1.517$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$1$	$2$		$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$
190.2.e.b	$2$	$1.517$	$\Q(\sqrt{-3}) $	None	$1$	$1$	$1$	$4$		$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
190.2.e.c	$4$	$1.517$	$\Q(\sqrt{-3}, \sqrt{17})$	None	$2$	$1$	$-2$	$10$		$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots$
190.2.f.a	$4$	$1.517$	$\Q(\zeta_{8})$	None	$0$	$0$	$-4$	$-4$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+2\zeta_{8}^{2})q^{5}+\cdots$
190.2.f.b	$16$	$1.517$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$0$	$8$		$q-\beta _{8}q^{2}+(\beta _{1}-\beta _{7}+\beta _{10}+\beta _{12})q^{3}+\cdots$
190.2.i.a	$20$	$1.517$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$0$	$0$	$-2$	$0$		$q+(-\beta _{2}-\beta _{13})q^{2}-\beta _{1}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$
190.2.k.a	$6$	$1.517$	$\Q(\zeta_{18})$	None	$0$	$3$	$0$	$0$		$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
190.2.k.b	$12$	$1.517$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$0$	$6$		$q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
190.2.k.c	$12$	$1.517$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$3$	$0$	$-6$		$q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots$
190.2.k.d	$18$	$1.517$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots$
190.2.m.a	$8$	$1.517$	$\Q(\zeta_{24})$	None	$0$	$12$	$4$	$-16$		$q+\zeta_{24}^{7}q^{2}+(2+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots$
190.2.m.b	$32$	$1.517$		None	$0$	$-12$	$0$	$24$
190.2.p.a	$60$	$1.517$		None	$0$	$0$	$0$	$0$
190.2.r.a	$120$	$1.517$		None	$0$	$0$	$0$	$-12$
190.3.c.a	$16$	$5.177$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$0$	$-8$		$q+\beta _{9}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots$
190.3.d.a	$20$	$5.177$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$0$	$0$	$-2$	$0$		$q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots$
190.3.g.a	$16$	$5.177$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-16$	$8$	$2$	$-10$		$q+(-1-\beta _{5})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots$
190.3.g.b	$20$	$5.177$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$20$	$0$	$2$	$14$		$q+(1+\beta _{3})q^{2}-\beta _{2}q^{3}+2\beta _{3}q^{4}+\beta _{16}q^{5}+\cdots$
190.3.h.a	$4$	$5.177$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$0$	$0$	$-2$	$0$		$q+\beta _{1}q^{2}+2\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
190.3.h.b	$36$	$5.177$		None	$0$	$0$	$4$	$0$
190.3.j.a	$32$	$5.177$		None	$0$	$-12$	$0$	$8$
190.3.l.a	$4$	$5.177$	$\Q(\zeta_{12})$	None	$-2$	$-6$	$8$	$32$		$q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+\cdots)q^{3}+\cdots$
190.3.l.b	$4$	$5.177$	$\Q(\zeta_{12})$	None	$2$	$6$	$10$	$8$		$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(3\zeta_{12}+\cdots)q^{3}+\cdots$
190.3.l.c	$36$	$5.177$		None	$-18$	$6$	$-10$	$-28$
190.3.l.d	$36$	$5.177$		None	$18$	$-6$	$-12$	$12$
190.3.n.a	$72$	$5.177$		None	$0$	$12$	$0$	$0$
190.3.o.a	$120$	$5.177$		None	$0$	$0$	$0$	$0$
190.3.q.a	$120$	$5.177$		None	$0$	$0$	$0$	$-18$
190.3.q.b	$120$	$5.177$		None	$0$	$0$	$0$	$-18$
190.4.a.a	$1$	$11.210$	$\Q$	None	$-2$	$-2$	$5$	$8$	$+$	$q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots$
190.4.a.b	$1$	$11.210$	$\Q$	None	$-2$	$2$	$5$	$-12$	$-$	$q-2q^{2}+2q^{3}+4q^{4}+5q^{5}-4q^{6}+\cdots$
190.4.a.c	$1$	$11.210$	$\Q$	None	$2$	$-4$	$5$	$-20$	$-$	$q+2q^{2}-4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots$
190.4.a.d	$2$	$11.210$	$\Q(\sqrt{313}) $	None	$-4$	$1$	$10$	$-27$	$+$	$q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots$
190.4.a.e	$2$	$11.210$	$\Q(\sqrt{3}) $	None	$-4$	$2$	$-10$	$8$	$+$	$q-2q^{2}+(1+3\beta )q^{3}+4q^{4}-5q^{5}+\cdots$
190.4.a.f	$2$	$11.210$	$\Q(\sqrt{34}) $	None	$4$	$0$	$-10$	$24$	$+$	$q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots$
190.4.a.g	$3$	$11.210$	3.3.126168.1	None	$-6$	$-1$	$-15$	$1$	$-$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots$
190.4.a.h	$3$	$11.210$	3.3.5468.1	None	$6$	$-9$	$-15$	$-11$	$-$	$q+2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$
190.4.a.i	$3$	$11.210$	3.3.15357.1	None	$6$	$11$	$15$	$29$	$+$	$q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots$
190.4.b.a	$12$	$11.210$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$20$	$0$		$q+\beta _{8}q^{2}+(\beta _{8}-\beta _{9})q^{3}-4q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots$
190.4.b.b	$14$	$11.210$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None	$0$	$0$	$-8$	$0$		$q-\beta _{8}q^{2}+\beta _{3}q^{3}-4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$
190.4.e.a	$2$	$11.210$	$\Q(\sqrt{-3}) $	None	$2$	$2$	$-5$	$-56$		$q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
190.4.e.b	$2$	$11.210$	$\Q(\sqrt{-3}) $	None	$2$	$2$	$5$	$64$		$q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
190.4.e.c	$6$	$11.210$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None	$6$	$3$	$-15$	$36$		$q+2\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots$
190.4.e.d	$8$	$11.210$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$8$	$3$	$20$	$-82$		$q+(2+2\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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
190.2.a.a	\(1\)	\(1.517\)	\(\Q\)	None	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.b	\(1\)	\(1.517\)	\(\Q\)	None	\(1\)	\(-3\)	\(-1\)	\(-5\)	\(+\)	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots\)
190.2.a.c	\(1\)	\(1.517\)	\(\Q\)	None	\(1\)	\(1\)	\(1\)	\(-1\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.d	\(2\)	\(1.517\)	\(\Q(\sqrt{17}) \)	None	\(-2\)	\(-1\)	\(2\)	\(-1\)	\(-\)	\(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)
190.2.b.a	\(4\)	\(1.517\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
190.2.b.b	\(6\)	\(1.517\)	6.0.5161984.1	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
190.2.e.a	\(2\)	\(1.517\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(1\)	\(2\)		\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
190.2.e.b	\(2\)	\(1.517\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(1\)	\(1\)	\(4\)		\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
190.2.e.c	\(4\)	\(1.517\)	\(\Q(\sqrt{-3}, \sqrt{17})\)	None	\(2\)	\(1\)	\(-2\)	\(10\)		\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
190.2.f.a	\(4\)	\(1.517\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(-4\)	\(-4\)		\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+2\zeta_{8}^{2})q^{5}+\cdots\)
190.2.f.b	\(16\)	\(1.517\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(8\)		\(q-\beta _{8}q^{2}+(\beta _{1}-\beta _{7}+\beta _{10}+\beta _{12})q^{3}+\cdots\)
190.2.i.a	\(20\)	\(1.517\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+(-\beta _{2}-\beta _{13})q^{2}-\beta _{1}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
190.2.k.a	\(6\)	\(1.517\)	\(\Q(\zeta_{18})\)	None	\(0\)	\(3\)	\(0\)	\(0\)		\(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
190.2.k.b	\(12\)	\(1.517\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(6\)		\(q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
190.2.k.c	\(12\)	\(1.517\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(3\)	\(0\)	\(-6\)		\(q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots\)
190.2.k.d	\(18\)	\(1.517\)	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots\)
190.2.m.a	\(8\)	\(1.517\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(12\)	\(4\)	\(-16\)		\(q+\zeta_{24}^{7}q^{2}+(2+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
190.2.m.b	\(32\)	\(1.517\)		None	\(0\)	\(-12\)	\(0\)	\(24\)
190.2.p.a	\(60\)	\(1.517\)		None	\(0\)	\(0\)	\(0\)	\(0\)
190.2.r.a	\(120\)	\(1.517\)		None	\(0\)	\(0\)	\(0\)	\(-12\)
190.3.c.a	\(16\)	\(5.177\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+\beta _{9}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots\)
190.3.d.a	\(20\)	\(5.177\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)
190.3.g.a	\(16\)	\(5.177\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-16\)	\(8\)	\(2\)	\(-10\)		\(q+(-1-\beta _{5})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots\)
190.3.g.b	\(20\)	\(5.177\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(20\)	\(0\)	\(2\)	\(14\)		\(q+(1+\beta _{3})q^{2}-\beta _{2}q^{3}+2\beta _{3}q^{4}+\beta _{16}q^{5}+\cdots\)
190.3.h.a	\(4\)	\(5.177\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+\beta _{1}q^{2}+2\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
190.3.h.b	\(36\)	\(5.177\)		None	\(0\)	\(0\)	\(4\)	\(0\)
190.3.j.a	\(32\)	\(5.177\)		None	\(0\)	\(-12\)	\(0\)	\(8\)
190.3.l.a	\(4\)	\(5.177\)	\(\Q(\zeta_{12})\)	None	\(-2\)	\(-6\)	\(8\)	\(32\)		\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+\cdots)q^{3}+\cdots\)
190.3.l.b	\(4\)	\(5.177\)	\(\Q(\zeta_{12})\)	None	\(2\)	\(6\)	\(10\)	\(8\)		\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(3\zeta_{12}+\cdots)q^{3}+\cdots\)
190.3.l.c	\(36\)	\(5.177\)		None	\(-18\)	\(6\)	\(-10\)	\(-28\)
190.3.l.d	\(36\)	\(5.177\)		None	\(18\)	\(-6\)	\(-12\)	\(12\)
190.3.n.a	\(72\)	\(5.177\)		None	\(0\)	\(12\)	\(0\)	\(0\)
190.3.o.a	\(120\)	\(5.177\)		None	\(0\)	\(0\)	\(0\)	\(0\)
190.3.q.a	\(120\)	\(5.177\)		None	\(0\)	\(0\)	\(0\)	\(-18\)
190.3.q.b	\(120\)	\(5.177\)		None	\(0\)	\(0\)	\(0\)	\(-18\)
190.4.a.a	\(1\)	\(11.210\)	\(\Q\)	None	\(-2\)	\(-2\)	\(5\)	\(8\)	\(+\)	\(q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots\)
190.4.a.b	\(1\)	\(11.210\)	\(\Q\)	None	\(-2\)	\(2\)	\(5\)	\(-12\)	\(-\)	\(q-2q^{2}+2q^{3}+4q^{4}+5q^{5}-4q^{6}+\cdots\)
190.4.a.c	\(1\)	\(11.210\)	\(\Q\)	None	\(2\)	\(-4\)	\(5\)	\(-20\)	\(-\)	\(q+2q^{2}-4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots\)
190.4.a.d	\(2\)	\(11.210\)	\(\Q(\sqrt{313}) \)	None	\(-4\)	\(1\)	\(10\)	\(-27\)	\(+\)	\(q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots\)
190.4.a.e	\(2\)	\(11.210\)	\(\Q(\sqrt{3}) \)	None	\(-4\)	\(2\)	\(-10\)	\(8\)	\(+\)	\(q-2q^{2}+(1+3\beta )q^{3}+4q^{4}-5q^{5}+\cdots\)
190.4.a.f	\(2\)	\(11.210\)	\(\Q(\sqrt{34}) \)	None	\(4\)	\(0\)	\(-10\)	\(24\)	\(+\)	\(q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots\)
190.4.a.g	\(3\)	\(11.210\)	3.3.126168.1	None	\(-6\)	\(-1\)	\(-15\)	\(1\)	\(-\)	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots\)
190.4.a.h	\(3\)	\(11.210\)	3.3.5468.1	None	\(6\)	\(-9\)	\(-15\)	\(-11\)	\(-\)	\(q+2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
190.4.a.i	\(3\)	\(11.210\)	3.3.15357.1	None	\(6\)	\(11\)	\(15\)	\(29\)	\(+\)	\(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
190.4.b.a	\(12\)	\(11.210\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(20\)	\(0\)		\(q+\beta _{8}q^{2}+(\beta _{8}-\beta _{9})q^{3}-4q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots\)
190.4.b.b	\(14\)	\(11.210\)	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None	\(0\)	\(0\)	\(-8\)	\(0\)		\(q-\beta _{8}q^{2}+\beta _{3}q^{3}-4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
190.4.e.a	\(2\)	\(11.210\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(2\)	\(-5\)	\(-56\)		\(q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
190.4.e.b	\(2\)	\(11.210\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(2\)	\(5\)	\(64\)		\(q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
190.4.e.c	\(6\)	\(11.210\)	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None	\(6\)	\(3\)	\(-15\)	\(36\)		\(q+2\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
190.4.e.d	\(8\)	\(11.210\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(8\)	\(3\)	\(20\)	\(-82\)		\(q+(2+2\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)

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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.