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 (displaying matches 1-50 of 207) 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
96.2.a.a	$1$	$0.767$	$\Q$	None	$0$	$-1$	$2$	$4$	$-$	$q-q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
96.2.a.b	$1$	$0.767$	$\Q$	None	$0$	$1$	$2$	$-4$	$-$	$q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
96.2.c.a	$4$	$0.767$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots$
96.2.d.a	$2$	$0.767$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$4$		$q+iq^{3}+2iq^{5}+2q^{7}-q^{9}-4iq^{13}+\cdots$
96.2.f.a	$2$	$0.767$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$2$	$0$	$0$		$q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-2\beta q^{11}+\cdots$
96.2.n.a	$32$	$0.767$		None	$0$	$0$	$0$	$0$
96.2.o.a	$56$	$0.767$		None	$0$	$-4$	$0$	$-8$
96.3.b.a	$4$	$2.616$	4.0.4752.1	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
96.3.e.a	$4$	$2.616$	$\Q(\sqrt{-2}, \sqrt{3})$	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(2\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots$
96.3.e.b	$4$	$2.616$	$\Q(\sqrt{-2}, \sqrt{7})$	None	$0$	$0$	$0$	$0$		$q+(\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots$
96.3.g.a	$4$	$2.616$	$\Q(\zeta_{12})$	None	$0$	$0$	$-8$	$0$		$q+\zeta_{12}^{2}q^{3}+(-2-\zeta_{12}^{3})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots$
96.3.h.a	$1$	$2.616$	$\Q$	$\Q(\sqrt{-6}) $	$0$	$-3$	$2$	$10$		$q-3q^{3}+2q^{5}+10q^{7}+9q^{9}+10q^{11}+\cdots$
96.3.h.b	$1$	$2.616$	$\Q$	$\Q(\sqrt{-6}) $	$0$	$3$	$-2$	$10$		$q+3q^{3}-2q^{5}+10q^{7}+9q^{9}-10q^{11}+\cdots$
96.3.h.c	$4$	$2.616$	$\Q(\sqrt{2}, \sqrt{-7})$	None	$0$	$0$	$0$	$-16$		$q+(-\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{5}-4q^{7}+\cdots$
96.3.m.a	$64$	$2.616$		None	$0$	$0$	$0$	$0$
96.3.p.a	$120$	$2.616$		None	$0$	$-4$	$0$	$-8$
96.4.a.a	$1$	$5.664$	$\Q$	None	$0$	$-3$	$-14$	$36$	$+$	$q-3q^{3}-14q^{5}+6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots$
96.4.a.b	$1$	$5.664$	$\Q$	None	$0$	$-3$	$2$	$-12$	$-$	$q-3q^{3}+2q^{5}-12q^{7}+9q^{9}-60q^{11}+\cdots$
96.4.a.c	$1$	$5.664$	$\Q$	None	$0$	$-3$	$10$	$-4$	$+$	$q-3q^{3}+10q^{5}-4q^{7}+9q^{9}+20q^{11}+\cdots$
96.4.a.d	$1$	$5.664$	$\Q$	None	$0$	$3$	$-14$	$-36$	$-$	$q+3q^{3}-14q^{5}-6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots$
96.4.a.e	$1$	$5.664$	$\Q$	None	$0$	$3$	$2$	$12$	$+$	$q+3q^{3}+2q^{5}+12q^{7}+9q^{9}+60q^{11}+\cdots$
96.4.a.f	$1$	$5.664$	$\Q$	None	$0$	$3$	$10$	$4$	$+$	$q+3q^{3}+10q^{5}+4q^{7}+9q^{9}-20q^{11}+\cdots$
96.4.c.a	$12$	$5.664$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{4}q^{3}-\beta _{8}q^{5}-\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots$
96.4.d.a	$6$	$5.664$	6.0.8248384.1	None	$0$	$0$	$0$	$-28$		$q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-5+\beta _{1}+\cdots)q^{7}+\cdots$
96.4.f.a	$2$	$5.664$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$-10$	$0$	$0$		$q+(-5+\beta )q^{3}+(23-10\beta )q^{9}-50\beta q^{11}+\cdots$
96.4.f.b	$8$	$5.664$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$12$	$0$	$0$		$q+(1+\beta _{2})q^{3}+\beta _{4}q^{5}-\beta _{6}q^{7}+(-9+\cdots)q^{9}+\cdots$
96.4.n.a	$96$	$5.664$		None	$0$	$0$	$0$	$0$
96.4.o.a	$184$	$5.664$		None	$0$	$-4$	$0$	$-8$
96.5.b.a	$8$	$9.924$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$
96.5.e.a	$8$	$9.924$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-11-2\beta _{2}+\cdots)q^{9}+\cdots$
96.5.e.b	$8$	$9.924$	8.0.3317760000.8	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots$
96.5.g.a	$4$	$9.924$	$\Q(\zeta_{12})$	None	$0$	$0$	$-40$	$0$		$q+3\zeta_{12}^{2}q^{3}+(-10-\zeta_{12}^{3})q^{5}+(11\zeta_{12}+\cdots)q^{7}+\cdots$
96.5.g.b	$4$	$9.924$	$\Q(\zeta_{12})$	None	$0$	$0$	$88$	$0$		$q-\zeta_{12}^{2}q^{3}+(22-\zeta_{12}^{3})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots$
96.5.h.a	$1$	$9.924$	$\Q$	$\Q(\sqrt{-6}) $	$0$	$-9$	$-46$	$-2$		$q-9q^{3}-46q^{5}-2q^{7}+3^{4}q^{9}+142q^{11}+\cdots$
96.5.h.b	$1$	$9.924$	$\Q$	$\Q(\sqrt{-6}) $	$0$	$9$	$46$	$-2$		$q+9q^{3}+46q^{5}-2q^{7}+3^{4}q^{9}-142q^{11}+\cdots$
96.5.h.c	$12$	$9.924$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$0$	$8$		$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{4})q^{7}+\cdots$
96.5.m.a	$128$	$9.924$		None	$0$	$0$	$0$	$0$
96.5.p.a	$248$	$9.924$		None	$0$	$-4$	$0$	$-8$
96.6.a.a	$1$	$15.397$	$\Q$	None	$0$	$-9$	$-86$	$-180$	$-$	$q-9q^{3}-86q^{5}-180q^{7}+3^{4}q^{9}+\cdots$
96.6.a.b	$1$	$15.397$	$\Q$	None	$0$	$-9$	$-14$	$100$	$+$	$q-9q^{3}-14q^{5}+10^{2}q^{7}+3^{4}q^{9}+\cdots$
96.6.a.c	$1$	$15.397$	$\Q$	None	$0$	$-9$	$26$	$-36$	$+$	$q-9q^{3}+26q^{5}-6^{2}q^{7}+3^{4}q^{9}-180q^{11}+\cdots$
96.6.a.d	$1$	$15.397$	$\Q$	None	$0$	$9$	$-86$	$180$	$+$	$q+9q^{3}-86q^{5}+180q^{7}+3^{4}q^{9}+\cdots$
96.6.a.e	$1$	$15.397$	$\Q$	None	$0$	$9$	$-14$	$-100$	$+$	$q+9q^{3}-14q^{5}-10^{2}q^{7}+3^{4}q^{9}+\cdots$
96.6.a.f	$1$	$15.397$	$\Q$	None	$0$	$9$	$26$	$36$	$-$	$q+9q^{3}+26q^{5}+6^{2}q^{7}+3^{4}q^{9}+180q^{11}+\cdots$
96.6.a.g	$2$	$15.397$	$\Q(\sqrt{31}) $	None	$0$	$-18$	$36$	$-120$	$-$	$q-9q^{3}+(18+\beta )q^{5}+(-60-\beta )q^{7}+\cdots$
96.6.a.h	$2$	$15.397$	$\Q(\sqrt{31}) $	None	$0$	$18$	$36$	$120$	$-$	$q+9q^{3}+(18+\beta )q^{5}+(60+\beta )q^{7}+3^{4}q^{9}+\cdots$
96.6.c.a	$20$	$15.397$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{3}q^{3}+\beta _{6}q^{5}+\beta _{2}q^{7}+(-2-\beta _{7}+\cdots)q^{9}+\cdots$
96.6.d.a	$10$	$15.397$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$0$	$0$	$196$		$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(20+\beta _{4}+\cdots)q^{7}+\cdots$
96.6.f.a	$2$	$15.397$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$2$	$0$	$0$		$q+(1-11\beta )q^{3}+(-241-22\beta )q^{9}+\cdots$
96.6.f.b	$16$	$15.397$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{4}q^{7}+(30+\beta _{7}+\cdots)q^{9}+\cdots$

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
96.2.a.a	\(1\)	\(0.767\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(4\)	\(-\)	\(q-q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
96.2.a.b	\(1\)	\(0.767\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(-4\)	\(-\)	\(q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
96.2.c.a	\(4\)	\(0.767\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots\)
96.2.d.a	\(2\)	\(0.767\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q+iq^{3}+2iq^{5}+2q^{7}-q^{9}-4iq^{13}+\cdots\)
96.2.f.a	\(2\)	\(0.767\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(2\)	\(0\)	\(0\)		\(q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-2\beta q^{11}+\cdots\)
96.2.n.a	\(32\)	\(0.767\)		None	\(0\)	\(0\)	\(0\)	\(0\)
96.2.o.a	\(56\)	\(0.767\)		None	\(0\)	\(-4\)	\(0\)	\(-8\)
96.3.b.a	\(4\)	\(2.616\)	4.0.4752.1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots\)
96.3.e.a	\(4\)	\(2.616\)	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(2\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots\)
96.3.e.b	\(4\)	\(2.616\)	\(\Q(\sqrt{-2}, \sqrt{7})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots\)
96.3.g.a	\(4\)	\(2.616\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(-8\)	\(0\)		\(q+\zeta_{12}^{2}q^{3}+(-2-\zeta_{12}^{3})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
96.3.h.a	\(1\)	\(2.616\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(0\)	\(-3\)	\(2\)	\(10\)		\(q-3q^{3}+2q^{5}+10q^{7}+9q^{9}+10q^{11}+\cdots\)
96.3.h.b	\(1\)	\(2.616\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(0\)	\(3\)	\(-2\)	\(10\)		\(q+3q^{3}-2q^{5}+10q^{7}+9q^{9}-10q^{11}+\cdots\)
96.3.h.c	\(4\)	\(2.616\)	\(\Q(\sqrt{2}, \sqrt{-7})\)	None	\(0\)	\(0\)	\(0\)	\(-16\)		\(q+(-\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{5}-4q^{7}+\cdots\)
96.3.m.a	\(64\)	\(2.616\)		None	\(0\)	\(0\)	\(0\)	\(0\)
96.3.p.a	\(120\)	\(2.616\)		None	\(0\)	\(-4\)	\(0\)	\(-8\)
96.4.a.a	\(1\)	\(5.664\)	\(\Q\)	None	\(0\)	\(-3\)	\(-14\)	\(36\)	\(+\)	\(q-3q^{3}-14q^{5}+6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
96.4.a.b	\(1\)	\(5.664\)	\(\Q\)	None	\(0\)	\(-3\)	\(2\)	\(-12\)	\(-\)	\(q-3q^{3}+2q^{5}-12q^{7}+9q^{9}-60q^{11}+\cdots\)
96.4.a.c	\(1\)	\(5.664\)	\(\Q\)	None	\(0\)	\(-3\)	\(10\)	\(-4\)	\(+\)	\(q-3q^{3}+10q^{5}-4q^{7}+9q^{9}+20q^{11}+\cdots\)
96.4.a.d	\(1\)	\(5.664\)	\(\Q\)	None	\(0\)	\(3\)	\(-14\)	\(-36\)	\(-\)	\(q+3q^{3}-14q^{5}-6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
96.4.a.e	\(1\)	\(5.664\)	\(\Q\)	None	\(0\)	\(3\)	\(2\)	\(12\)	\(+\)	\(q+3q^{3}+2q^{5}+12q^{7}+9q^{9}+60q^{11}+\cdots\)
96.4.a.f	\(1\)	\(5.664\)	\(\Q\)	None	\(0\)	\(3\)	\(10\)	\(4\)	\(+\)	\(q+3q^{3}+10q^{5}+4q^{7}+9q^{9}-20q^{11}+\cdots\)
96.4.c.a	\(12\)	\(5.664\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{4}q^{3}-\beta _{8}q^{5}-\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)
96.4.d.a	\(6\)	\(5.664\)	6.0.8248384.1	None	\(0\)	\(0\)	\(0\)	\(-28\)		\(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-5+\beta _{1}+\cdots)q^{7}+\cdots\)
96.4.f.a	\(2\)	\(5.664\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(-10\)	\(0\)	\(0\)		\(q+(-5+\beta )q^{3}+(23-10\beta )q^{9}-50\beta q^{11}+\cdots\)
96.4.f.b	\(8\)	\(5.664\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(12\)	\(0\)	\(0\)		\(q+(1+\beta _{2})q^{3}+\beta _{4}q^{5}-\beta _{6}q^{7}+(-9+\cdots)q^{9}+\cdots\)
96.4.n.a	\(96\)	\(5.664\)		None	\(0\)	\(0\)	\(0\)	\(0\)
96.4.o.a	\(184\)	\(5.664\)		None	\(0\)	\(-4\)	\(0\)	\(-8\)
96.5.b.a	\(8\)	\(9.924\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
96.5.e.a	\(8\)	\(9.924\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-11-2\beta _{2}+\cdots)q^{9}+\cdots\)
96.5.e.b	\(8\)	\(9.924\)	8.0.3317760000.8	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots\)
96.5.g.a	\(4\)	\(9.924\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(-40\)	\(0\)		\(q+3\zeta_{12}^{2}q^{3}+(-10-\zeta_{12}^{3})q^{5}+(11\zeta_{12}+\cdots)q^{7}+\cdots\)
96.5.g.b	\(4\)	\(9.924\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(88\)	\(0\)		\(q-\zeta_{12}^{2}q^{3}+(22-\zeta_{12}^{3})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
96.5.h.a	\(1\)	\(9.924\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(0\)	\(-9\)	\(-46\)	\(-2\)		\(q-9q^{3}-46q^{5}-2q^{7}+3^{4}q^{9}+142q^{11}+\cdots\)
96.5.h.b	\(1\)	\(9.924\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(0\)	\(9\)	\(46\)	\(-2\)		\(q+9q^{3}+46q^{5}-2q^{7}+3^{4}q^{9}-142q^{11}+\cdots\)
96.5.h.c	\(12\)	\(9.924\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(8\)		\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{4})q^{7}+\cdots\)
96.5.m.a	\(128\)	\(9.924\)		None	\(0\)	\(0\)	\(0\)	\(0\)
96.5.p.a	\(248\)	\(9.924\)		None	\(0\)	\(-4\)	\(0\)	\(-8\)
96.6.a.a	\(1\)	\(15.397\)	\(\Q\)	None	\(0\)	\(-9\)	\(-86\)	\(-180\)	\(-\)	\(q-9q^{3}-86q^{5}-180q^{7}+3^{4}q^{9}+\cdots\)
96.6.a.b	\(1\)	\(15.397\)	\(\Q\)	None	\(0\)	\(-9\)	\(-14\)	\(100\)	\(+\)	\(q-9q^{3}-14q^{5}+10^{2}q^{7}+3^{4}q^{9}+\cdots\)
96.6.a.c	\(1\)	\(15.397\)	\(\Q\)	None	\(0\)	\(-9\)	\(26\)	\(-36\)	\(+\)	\(q-9q^{3}+26q^{5}-6^{2}q^{7}+3^{4}q^{9}-180q^{11}+\cdots\)
96.6.a.d	\(1\)	\(15.397\)	\(\Q\)	None	\(0\)	\(9\)	\(-86\)	\(180\)	\(+\)	\(q+9q^{3}-86q^{5}+180q^{7}+3^{4}q^{9}+\cdots\)
96.6.a.e	\(1\)	\(15.397\)	\(\Q\)	None	\(0\)	\(9\)	\(-14\)	\(-100\)	\(+\)	\(q+9q^{3}-14q^{5}-10^{2}q^{7}+3^{4}q^{9}+\cdots\)
96.6.a.f	\(1\)	\(15.397\)	\(\Q\)	None	\(0\)	\(9\)	\(26\)	\(36\)	\(-\)	\(q+9q^{3}+26q^{5}+6^{2}q^{7}+3^{4}q^{9}+180q^{11}+\cdots\)
96.6.a.g	\(2\)	\(15.397\)	\(\Q(\sqrt{31}) \)	None	\(0\)	\(-18\)	\(36\)	\(-120\)	\(-\)	\(q-9q^{3}+(18+\beta )q^{5}+(-60-\beta )q^{7}+\cdots\)
96.6.a.h	\(2\)	\(15.397\)	\(\Q(\sqrt{31}) \)	None	\(0\)	\(18\)	\(36\)	\(120\)	\(-\)	\(q+9q^{3}+(18+\beta )q^{5}+(60+\beta )q^{7}+3^{4}q^{9}+\cdots\)
96.6.c.a	\(20\)	\(15.397\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{3}q^{3}+\beta _{6}q^{5}+\beta _{2}q^{7}+(-2-\beta _{7}+\cdots)q^{9}+\cdots\)
96.6.d.a	\(10\)	\(15.397\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(196\)		\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(20+\beta _{4}+\cdots)q^{7}+\cdots\)
96.6.f.a	\(2\)	\(15.397\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(2\)	\(0\)	\(0\)		\(q+(1-11\beta )q^{3}+(-241-22\beta )q^{9}+\cdots\)
96.6.f.b	\(16\)	\(15.397\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{4}q^{7}+(30+\beta _{7}+\cdots)q^{9}+\cdots\)

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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.