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 227) 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
24.2.a.a	$1$	$0.192$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
24.2.d.a	$2$	$0.192$	$\Q(\sqrt{-1}) $	None	$-2$	$0$	$0$	$-4$		$q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots$
24.2.f.a	$2$	$0.192$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$-2$	$0$	$0$		$q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots$
24.3.b.a	$4$	$0.654$	4.0.4752.1	None	$2$	$0$	$0$	$0$		$q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots$
24.3.e.a	$2$	$0.654$	$\Q(\sqrt{-2}) $	None	$0$	$2$	$0$	$-12$		$q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots$
24.3.h.a	$1$	$0.654$	$\Q$	$\Q(\sqrt{-6}) $	$-2$	$3$	$2$	$-10$		$q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots$
24.3.h.b	$1$	$0.654$	$\Q$	$\Q(\sqrt{-6}) $	$2$	$-3$	$-2$	$-10$		$q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots$
24.3.h.c	$4$	$0.654$	$\Q(\sqrt{2}, \sqrt{-7})$	None	$0$	$0$	$0$	$16$		$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots$
24.4.a.a	$1$	$1.416$	$\Q$	None	$0$	$3$	$14$	$-24$	$+$	$q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots$
24.4.d.a	$6$	$1.416$	6.0.8248384.1	None	$2$	$0$	$0$	$28$		$q+\beta _{3}q^{2}+\beta _{1}q^{3}+(3-\beta _{5})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots$
24.4.f.a	$2$	$1.416$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$10$	$0$	$0$		$q+2\beta q^{2}+(5+\beta )q^{3}-8q^{4}+(-4+10\beta )q^{6}+\cdots$
24.4.f.b	$8$	$1.416$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$-12$	$0$	$0$		$q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(3+\beta _{2})q^{4}+\cdots$
24.5.b.a	$8$	$2.481$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$-6$	$0$	$0$	$0$		$q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
24.5.e.a	$4$	$2.481$	$\Q(\sqrt{-2}, \sqrt{13})$	None	$0$	$-4$	$0$	$24$		$q+(-1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots$
24.5.h.a	$1$	$2.481$	$\Q$	$\Q(\sqrt{-6}) $	$-4$	$-9$	$46$	$2$		$q-4q^{2}-9q^{3}+2^{4}q^{4}+46q^{5}+6^{2}q^{6}+\cdots$
24.5.h.b	$1$	$2.481$	$\Q$	$\Q(\sqrt{-6}) $	$4$	$9$	$-46$	$2$		$q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots$
24.5.h.c	$12$	$2.481$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$0$	$-8$		$q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
24.6.a.a	$1$	$3.849$	$\Q$	None	$0$	$-9$	$-34$	$-240$	$+$	$q-9q^{3}-34q^{5}-240q^{7}+3^{4}q^{9}+\cdots$
24.6.a.b	$1$	$3.849$	$\Q$	None	$0$	$-9$	$94$	$144$	$-$	$q-9q^{3}+94q^{5}+12^{2}q^{7}+3^{4}q^{9}+\cdots$
24.6.a.c	$1$	$3.849$	$\Q$	None	$0$	$9$	$38$	$120$	$-$	$q+9q^{3}+38q^{5}+120q^{7}+3^{4}q^{9}+\cdots$
24.6.d.a	$10$	$3.849$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$2$	$0$	$0$	$-196$		$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
24.6.f.a	$2$	$3.849$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$-2$	$0$	$0$		$q+4\beta q^{2}+(-1+11\beta )q^{3}-2^{5}q^{4}+\cdots$
24.6.f.b	$16$	$3.849$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(3+\beta _{2}+\cdots)q^{4}+\cdots$
24.7.b.a	$12$	$5.521$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$10$	$0$	$0$	$0$		$q+(1+\beta _{1})q^{2}-\beta _{2}q^{3}+(2+\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots$
24.7.e.a	$6$	$5.521$	6.0.1173604352.2	None	$0$	$-10$	$0$	$156$		$q+(-2+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(3^{3}+\cdots)q^{7}+\cdots$
24.7.h.a	$1$	$5.521$	$\Q$	$\Q(\sqrt{-6}) $	$-8$	$27$	$-142$	$470$		$q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-142q^{5}+\cdots$
24.7.h.b	$1$	$5.521$	$\Q$	$\Q(\sqrt{-6}) $	$8$	$-27$	$142$	$470$		$q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+142q^{5}+\cdots$
24.7.h.c	$20$	$5.521$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$0$	$0$	$0$	$-944$		$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-10+\beta _{3})q^{4}+\cdots$
24.8.a.a	$1$	$7.497$	$\Q$	None	$0$	$-27$	$-26$	$1056$	$+$	$q-3^{3}q^{3}-26q^{5}+1056q^{7}+3^{6}q^{9}+\cdots$
24.8.a.b	$1$	$7.497$	$\Q$	None	$0$	$27$	$-530$	$120$	$-$	$q+3^{3}q^{3}-530q^{5}+120q^{7}+3^{6}q^{9}+\cdots$
24.8.a.c	$1$	$7.497$	$\Q$	None	$0$	$27$	$110$	$504$	$+$	$q+3^{3}q^{3}+110q^{5}+504q^{7}+3^{6}q^{9}+\cdots$
24.8.d.a	$14$	$7.497$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$-14$	$0$	$0$	$1372$		$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(-15-\beta _{1}+\cdots)q^{4}+\cdots$
24.8.f.a	$2$	$7.497$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$-86$	$0$	$0$		$q+8\beta q^{2}+(-43+13\beta )q^{3}-2^{7}q^{4}+\cdots$
24.8.f.b	$4$	$7.497$	$\Q(\sqrt{6}, \sqrt{-26})$	None	$0$	$-36$	$0$	$0$		$q+(2\beta _{1}+\beta _{2})q^{2}+(-9-9\beta _{1})q^{3}+(-80+\cdots)q^{4}+\cdots$
24.8.f.c	$20$	$7.497$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$0$	$120$	$0$	$0$		$q+\beta _{1}q^{2}+(6+\beta _{1}-\beta _{4})q^{3}+(3^{3}+\beta _{3}+\cdots)q^{4}+\cdots$
24.9.b.a	$16$	$9.777$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-6$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(26-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
24.9.e.a	$8$	$9.777$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$56$	$0$	$1584$		$q+(7+\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(198+\cdots)q^{7}+\cdots$
24.9.h.a	$1$	$9.777$	$\Q$	$\Q(\sqrt{-6}) $	$-16$	$-81$	$-866$	$-4798$		$q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-866q^{5}+\cdots$
24.9.h.b	$1$	$9.777$	$\Q$	$\Q(\sqrt{-6}) $	$16$	$81$	$866$	$-4798$		$q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+866q^{5}+\cdots$
24.9.h.c	$28$	$9.777$		None	$0$	$0$	$0$	$9592$
24.10.a.a	$1$	$12.361$	$\Q$	None	$0$	$-81$	$830$	$672$	$+$	$q-3^{4}q^{3}+830q^{5}+672q^{7}+3^{8}q^{9}+\cdots$
24.10.a.b	$1$	$12.361$	$\Q$	None	$0$	$81$	$-794$	$-5880$	$+$	$q+3^{4}q^{3}-794q^{5}-5880q^{7}+3^{8}q^{9}+\cdots$
24.10.a.c	$1$	$12.361$	$\Q$	None	$0$	$81$	$614$	$2184$	$-$	$q+3^{4}q^{3}+614q^{5}+2184q^{7}+3^{8}q^{9}+\cdots$
24.10.a.d	$2$	$12.361$	$\Q(\sqrt{109}) $	None	$0$	$-162$	$-772$	$-2880$	$-$	$q-3^{4}q^{3}+(-386-\beta )q^{5}+(-1440+\cdots)q^{7}+\cdots$
24.10.d.a	$18$	$12.361$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$34$	$0$	$0$	$-9604$		$q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(29-2\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots$
24.10.f.a	$2$	$12.361$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$190$	$0$	$0$		$q+2^{4}\beta q^{2}+(95-73\beta )q^{3}-2^{9}q^{4}+\cdots$
24.10.f.b	$32$	$12.361$		None	$0$	$-192$	$0$	$0$
24.11.b.a	$20$	$15.249$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$-22$	$0$	$0$	$0$		$q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+(-93-\beta _{1}+\cdots)q^{4}+\cdots$
24.11.e.a	$10$	$15.249$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$-22$	$0$	$-5436$		$q+(-2+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-545+\cdots)q^{7}+\cdots$
24.11.h.a	$1$	$15.249$	$\Q$	$\Q(\sqrt{-6}) $	$-32$	$243$	$5282$	$24950$		$q-2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+5282q^{5}+\cdots$

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
24.2.a.a	\(1\)	\(0.192\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
24.2.d.a	\(2\)	\(0.192\)	\(\Q(\sqrt{-1}) \)	None	\(-2\)	\(0\)	\(0\)	\(-4\)		\(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)
24.2.f.a	\(2\)	\(0.192\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(-2\)	\(0\)	\(0\)		\(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)
24.3.b.a	\(4\)	\(0.654\)	4.0.4752.1	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
24.3.e.a	\(2\)	\(0.654\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(2\)	\(0\)	\(-12\)		\(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)
24.3.h.a	\(1\)	\(0.654\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(-2\)	\(3\)	\(2\)	\(-10\)		\(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b	\(1\)	\(0.654\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(2\)	\(-3\)	\(-2\)	\(-10\)		\(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c	\(4\)	\(0.654\)	\(\Q(\sqrt{2}, \sqrt{-7})\)	None	\(0\)	\(0\)	\(0\)	\(16\)		\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
24.4.a.a	\(1\)	\(1.416\)	\(\Q\)	None	\(0\)	\(3\)	\(14\)	\(-24\)	\(+\)	\(q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots\)
24.4.d.a	\(6\)	\(1.416\)	6.0.8248384.1	None	\(2\)	\(0\)	\(0\)	\(28\)		\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(3-\beta _{5})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
24.4.f.a	\(2\)	\(1.416\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(10\)	\(0\)	\(0\)		\(q+2\beta q^{2}+(5+\beta )q^{3}-8q^{4}+(-4+10\beta )q^{6}+\cdots\)
24.4.f.b	\(8\)	\(1.416\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(-12\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
24.5.b.a	\(8\)	\(2.481\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(-6\)	\(0\)	\(0\)	\(0\)		\(q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
24.5.e.a	\(4\)	\(2.481\)	\(\Q(\sqrt{-2}, \sqrt{13})\)	None	\(0\)	\(-4\)	\(0\)	\(24\)		\(q+(-1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
24.5.h.a	\(1\)	\(2.481\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(-4\)	\(-9\)	\(46\)	\(2\)		\(q-4q^{2}-9q^{3}+2^{4}q^{4}+46q^{5}+6^{2}q^{6}+\cdots\)
24.5.h.b	\(1\)	\(2.481\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(4\)	\(9\)	\(-46\)	\(2\)		\(q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots\)
24.5.h.c	\(12\)	\(2.481\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
24.6.a.a	\(1\)	\(3.849\)	\(\Q\)	None	\(0\)	\(-9\)	\(-34\)	\(-240\)	\(+\)	\(q-9q^{3}-34q^{5}-240q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.b	\(1\)	\(3.849\)	\(\Q\)	None	\(0\)	\(-9\)	\(94\)	\(144\)	\(-\)	\(q-9q^{3}+94q^{5}+12^{2}q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.c	\(1\)	\(3.849\)	\(\Q\)	None	\(0\)	\(9\)	\(38\)	\(120\)	\(-\)	\(q+9q^{3}+38q^{5}+120q^{7}+3^{4}q^{9}+\cdots\)
24.6.d.a	\(10\)	\(3.849\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(2\)	\(0\)	\(0\)	\(-196\)		\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
24.6.f.a	\(2\)	\(3.849\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(-2\)	\(0\)	\(0\)		\(q+4\beta q^{2}+(-1+11\beta )q^{3}-2^{5}q^{4}+\cdots\)
24.6.f.b	\(16\)	\(3.849\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(3+\beta _{2}+\cdots)q^{4}+\cdots\)
24.7.b.a	\(12\)	\(5.521\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(10\)	\(0\)	\(0\)	\(0\)		\(q+(1+\beta _{1})q^{2}-\beta _{2}q^{3}+(2+\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
24.7.e.a	\(6\)	\(5.521\)	6.0.1173604352.2	None	\(0\)	\(-10\)	\(0\)	\(156\)		\(q+(-2+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(3^{3}+\cdots)q^{7}+\cdots\)
24.7.h.a	\(1\)	\(5.521\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(-8\)	\(27\)	\(-142\)	\(470\)		\(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-142q^{5}+\cdots\)
24.7.h.b	\(1\)	\(5.521\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(8\)	\(-27\)	\(142\)	\(470\)		\(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+142q^{5}+\cdots\)
24.7.h.c	\(20\)	\(5.521\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-944\)		\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-10+\beta _{3})q^{4}+\cdots\)
24.8.a.a	\(1\)	\(7.497\)	\(\Q\)	None	\(0\)	\(-27\)	\(-26\)	\(1056\)	\(+\)	\(q-3^{3}q^{3}-26q^{5}+1056q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.b	\(1\)	\(7.497\)	\(\Q\)	None	\(0\)	\(27\)	\(-530\)	\(120\)	\(-\)	\(q+3^{3}q^{3}-530q^{5}+120q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.c	\(1\)	\(7.497\)	\(\Q\)	None	\(0\)	\(27\)	\(110\)	\(504\)	\(+\)	\(q+3^{3}q^{3}+110q^{5}+504q^{7}+3^{6}q^{9}+\cdots\)
24.8.d.a	\(14\)	\(7.497\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(-14\)	\(0\)	\(0\)	\(1372\)		\(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(-15-\beta _{1}+\cdots)q^{4}+\cdots\)
24.8.f.a	\(2\)	\(7.497\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(-86\)	\(0\)	\(0\)		\(q+8\beta q^{2}+(-43+13\beta )q^{3}-2^{7}q^{4}+\cdots\)
24.8.f.b	\(4\)	\(7.497\)	\(\Q(\sqrt{6}, \sqrt{-26})\)	None	\(0\)	\(-36\)	\(0\)	\(0\)		\(q+(2\beta _{1}+\beta _{2})q^{2}+(-9-9\beta _{1})q^{3}+(-80+\cdots)q^{4}+\cdots\)
24.8.f.c	\(20\)	\(7.497\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(0\)	\(120\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(6+\beta _{1}-\beta _{4})q^{3}+(3^{3}+\beta _{3}+\cdots)q^{4}+\cdots\)
24.9.b.a	\(16\)	\(9.777\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-6\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(26-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
24.9.e.a	\(8\)	\(9.777\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(56\)	\(0\)	\(1584\)		\(q+(7+\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(198+\cdots)q^{7}+\cdots\)
24.9.h.a	\(1\)	\(9.777\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(-16\)	\(-81\)	\(-866\)	\(-4798\)		\(q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-866q^{5}+\cdots\)
24.9.h.b	\(1\)	\(9.777\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(16\)	\(81\)	\(866\)	\(-4798\)		\(q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+866q^{5}+\cdots\)
24.9.h.c	\(28\)	\(9.777\)		None	\(0\)	\(0\)	\(0\)	\(9592\)
24.10.a.a	\(1\)	\(12.361\)	\(\Q\)	None	\(0\)	\(-81\)	\(830\)	\(672\)	\(+\)	\(q-3^{4}q^{3}+830q^{5}+672q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.b	\(1\)	\(12.361\)	\(\Q\)	None	\(0\)	\(81\)	\(-794\)	\(-5880\)	\(+\)	\(q+3^{4}q^{3}-794q^{5}-5880q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.c	\(1\)	\(12.361\)	\(\Q\)	None	\(0\)	\(81\)	\(614\)	\(2184\)	\(-\)	\(q+3^{4}q^{3}+614q^{5}+2184q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.d	\(2\)	\(12.361\)	\(\Q(\sqrt{109}) \)	None	\(0\)	\(-162\)	\(-772\)	\(-2880\)	\(-\)	\(q-3^{4}q^{3}+(-386-\beta )q^{5}+(-1440+\cdots)q^{7}+\cdots\)
24.10.d.a	\(18\)	\(12.361\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(34\)	\(0\)	\(0\)	\(-9604\)		\(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(29-2\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots\)
24.10.f.a	\(2\)	\(12.361\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(190\)	\(0\)	\(0\)		\(q+2^{4}\beta q^{2}+(95-73\beta )q^{3}-2^{9}q^{4}+\cdots\)
24.10.f.b	\(32\)	\(12.361\)		None	\(0\)	\(-192\)	\(0\)	\(0\)
24.11.b.a	\(20\)	\(15.249\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(-22\)	\(0\)	\(0\)	\(0\)		\(q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+(-93-\beta _{1}+\cdots)q^{4}+\cdots\)
24.11.e.a	\(10\)	\(15.249\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(-22\)	\(0\)	\(-5436\)		\(q+(-2+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-545+\cdots)q^{7}+\cdots\)
24.11.h.a	\(1\)	\(15.249\)	\(\Q\)	\(\Q(\sqrt{-6}) \)	\(-32\)	\(243\)	\(5282\)	\(24950\)		\(q-2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+5282q^{5}+\cdots\)

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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.