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 266) 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
15.2.a.a	$1$	$0.120$	$\Q$	None	$-1$	$-1$	$1$	$0$	$-$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots$
15.3.c.a	$2$	$0.409$	$\Q(\sqrt{-5}) $	None	$0$	$-4$	$0$	$-12$		$q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots$
15.3.d.a	$1$	$0.409$	$\Q$	$\Q(\sqrt{-15}) $	$-1$	$3$	$-5$	$0$		$q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots$
15.3.d.b	$1$	$0.409$	$\Q$	$\Q(\sqrt{-15}) $	$1$	$-3$	$5$	$0$		$q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots$
15.3.f.a	$4$	$0.409$	$\Q(i, \sqrt{6})$	None	$-4$	$0$	$-4$	$4$		$q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
15.4.a.a	$1$	$0.885$	$\Q$	None	$1$	$3$	$5$	$-24$	$+$	$q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots$
15.4.a.b	$1$	$0.885$	$\Q$	None	$3$	$-3$	$-5$	$20$	$+$	$q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots$
15.4.b.a	$4$	$0.885$	$\Q(i, \sqrt{41})$	None	$0$	$0$	$6$	$0$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots$
15.4.e.a	$8$	$0.885$	8.0.$\cdots$.8	None	$0$	$-6$	$0$	$-16$		$q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$
15.5.c.a	$6$	$1.551$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None	$0$	$8$	$0$	$76$		$q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
15.5.d.a	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	$-7$	$9$	$25$	$0$		$q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.b	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	$7$	$-9$	$-25$	$0$		$q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.c	$4$	$1.551$	$\Q(\sqrt{10}, \sqrt{-26})$	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$
15.5.f.a	$8$	$1.551$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$0$	$-84$	$20$		$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots$
15.6.a.a	$1$	$2.406$	$\Q$	None	$-2$	$-9$	$-25$	$-132$	$+$	$q-2q^{2}-9q^{3}-28q^{4}-5^{2}q^{5}+18q^{6}+\cdots$
15.6.a.b	$1$	$2.406$	$\Q$	None	$7$	$9$	$-25$	$12$	$-$	$q+7q^{2}+9q^{3}+17q^{4}-5^{2}q^{5}+63q^{6}+\cdots$
15.6.a.c	$2$	$2.406$	$\Q(\sqrt{409}) $	None	$-1$	$-18$	$50$	$-112$	$-$	$q-\beta q^{2}-9q^{3}+(70+\beta )q^{4}+5^{2}q^{5}+\cdots$
15.6.b.a	$4$	$2.406$	$\Q(i, \sqrt{89})$	None	$0$	$0$	$120$	$0$		$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-11+\beta _{3})q^{4}+\cdots$
15.6.e.a	$16$	$2.406$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$0$	$-80$		$q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-13\beta _{3}-\beta _{6})q^{4}+\cdots$
15.7.c.a	$8$	$3.451$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$20$	$0$	$160$		$q-\beta _{2}q^{2}+(2-\beta _{5})q^{3}+(-41-\beta _{3}+\cdots)q^{4}+\cdots$
15.7.d.a	$1$	$3.451$	$\Q$	$\Q(\sqrt{-15}) $	$-11$	$-27$	$125$	$0$		$q-11q^{2}-3^{3}q^{3}+57q^{4}+5^{3}q^{5}+\cdots$
15.7.d.b	$1$	$3.451$	$\Q$	$\Q(\sqrt{-15}) $	$11$	$27$	$-125$	$0$		$q+11q^{2}+3^{3}q^{3}+57q^{4}-5^{3}q^{5}+\cdots$
15.7.d.c	$8$	$3.451$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{5}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots$
15.7.f.a	$12$	$3.451$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$16$	$0$	$136$	$-696$		$q+(1+\beta _{1}-\beta _{4})q^{2}-\beta _{6}q^{3}+(18\beta _{1}+\cdots)q^{4}+\cdots$
15.8.a.a	$1$	$4.686$	$\Q$	None	$-22$	$27$	$-125$	$-420$	$-$	$q-22q^{2}+3^{3}q^{3}+356q^{4}-5^{3}q^{5}+\cdots$
15.8.a.b	$1$	$4.686$	$\Q$	None	$-13$	$-27$	$-125$	$1380$	$+$	$q-13q^{2}-3^{3}q^{3}+41q^{4}-5^{3}q^{5}+\cdots$
15.8.a.c	$2$	$4.686$	$\Q(\sqrt{601}) $	None	$7$	$54$	$250$	$1304$	$+$	$q+(4-\beta )q^{2}+3^{3}q^{3}+(38-7\beta )q^{4}+\cdots$
15.8.b.a	$8$	$4.686$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$0$	$0$	$-444$	$0$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-83-\beta _{4})q^{4}+\cdots$
15.8.e.a	$24$	$4.686$		None	$0$	$24$	$0$	$1344$
15.9.c.a	$10$	$6.111$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$-112$	$0$	$7156$		$q-\beta _{1}q^{2}+(-11-2\beta _{1}-\beta _{2})q^{3}+(-79+\cdots)q^{4}+\cdots$
15.9.d.a	$1$	$6.111$	$\Q$	$\Q(\sqrt{-15}) $	$-17$	$-81$	$-625$	$0$		$q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots$
15.9.d.b	$1$	$6.111$	$\Q$	$\Q(\sqrt{-15}) $	$17$	$81$	$625$	$0$		$q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots$
15.9.d.c	$12$	$6.111$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots$
15.9.f.a	$16$	$6.111$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$0$	$-444$	$4540$		$q+\beta _{2}q^{2}-\beta _{6}q^{3}+(158\beta _{1}-3\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots$
15.10.a.a	$1$	$7.726$	$\Q$	None	$-4$	$81$	$625$	$-7680$	$+$	$q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots$
15.10.a.b	$1$	$7.726$	$\Q$	None	$22$	$-81$	$-625$	$-5988$	$+$	$q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots$
15.10.a.c	$2$	$7.726$	$\Q(\sqrt{4729}) $	None	$19$	$162$	$-1250$	$-11872$	$-$	$q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots$
15.10.a.d	$2$	$7.726$	$\Q(\sqrt{241}) $	None	$31$	$-162$	$1250$	$14112$	$-$	$q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots$
15.10.b.a	$8$	$7.726$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$0$	$0$	$-690$	$0$		$q-\beta _{3}q^{2}+\beta _{4}q^{3}+(-149-\beta _{1})q^{4}+\cdots$
15.10.e.a	$32$	$7.726$		None	$0$	$-150$	$0$	$-9760$
15.11.c.a	$14$	$9.530$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None	$0$	$44$	$0$	$-50548$		$q-\beta _{2}q^{2}+(3+\beta _{2}-\beta _{3})q^{3}+(-629+\cdots)q^{4}+\cdots$
15.11.d.a	$1$	$9.530$	$\Q$	$\Q(\sqrt{-15}) $	$-61$	$243$	$-3125$	$0$		$q-61q^{2}+3^{5}q^{3}+2697q^{4}-5^{5}q^{5}+\cdots$
15.11.d.b	$1$	$9.530$	$\Q$	$\Q(\sqrt{-15}) $	$61$	$-243$	$3125$	$0$		$q+61q^{2}-3^{5}q^{3}+2697q^{4}+5^{5}q^{5}+\cdots$
15.11.d.c	$16$	$9.530$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{6}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(137-\beta _{2}+\cdots)q^{4}+\cdots$
15.11.f.a	$20$	$9.530$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$-64$	$0$	$10676$	$10604$		$q+(-3-3\beta _{2}-\beta _{3})q^{2}+\beta _{6}q^{3}+(451\beta _{2}+\cdots)q^{4}+\cdots$
15.12.a.a	$1$	$11.525$	$\Q$	None	$-56$	$-243$	$3125$	$27984$	$-$	$q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots$
15.12.a.b	$2$	$11.525$	$\Q(\sqrt{1609}) $	None	$-22$	$486$	$-6250$	$-10864$	$-$	$q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots$
15.12.a.c	$2$	$11.525$	$\Q(\sqrt{1801}) $	None	$-13$	$-486$	$-6250$	$7784$	$+$	$q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots$
15.12.a.d	$3$	$11.525$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-1$	$729$	$9375$	$-14608$	$+$	$q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots$
15.12.b.a	$12$	$11.525$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$2556$	$0$		$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots$

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
15.2.a.a	\(1\)	\(0.120\)	\(\Q\)	None	\(-1\)	\(-1\)	\(1\)	\(0\)	\(-\)	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
15.3.c.a	\(2\)	\(0.409\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(-4\)	\(0\)	\(-12\)		\(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)
15.3.d.a	\(1\)	\(0.409\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(-1\)	\(3\)	\(-5\)	\(0\)		\(q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots\)
15.3.d.b	\(1\)	\(0.409\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(1\)	\(-3\)	\(5\)	\(0\)		\(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)
15.3.f.a	\(4\)	\(0.409\)	\(\Q(i, \sqrt{6})\)	None	\(-4\)	\(0\)	\(-4\)	\(4\)		\(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
15.4.a.a	\(1\)	\(0.885\)	\(\Q\)	None	\(1\)	\(3\)	\(5\)	\(-24\)	\(+\)	\(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
15.4.a.b	\(1\)	\(0.885\)	\(\Q\)	None	\(3\)	\(-3\)	\(-5\)	\(20\)	\(+\)	\(q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots\)
15.4.b.a	\(4\)	\(0.885\)	\(\Q(i, \sqrt{41})\)	None	\(0\)	\(0\)	\(6\)	\(0\)		\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
15.4.e.a	\(8\)	\(0.885\)	8.0.\(\cdots\).8	None	\(0\)	\(-6\)	\(0\)	\(-16\)		\(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
15.5.c.a	\(6\)	\(1.551\)	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None	\(0\)	\(8\)	\(0\)	\(76\)		\(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
15.5.d.a	\(1\)	\(1.551\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(-7\)	\(9\)	\(25\)	\(0\)		\(q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.b	\(1\)	\(1.551\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(7\)	\(-9\)	\(-25\)	\(0\)		\(q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.c	\(4\)	\(1.551\)	\(\Q(\sqrt{10}, \sqrt{-26})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
15.5.f.a	\(8\)	\(1.551\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(0\)	\(-84\)	\(20\)		\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
15.6.a.a	\(1\)	\(2.406\)	\(\Q\)	None	\(-2\)	\(-9\)	\(-25\)	\(-132\)	\(+\)	\(q-2q^{2}-9q^{3}-28q^{4}-5^{2}q^{5}+18q^{6}+\cdots\)
15.6.a.b	\(1\)	\(2.406\)	\(\Q\)	None	\(7\)	\(9\)	\(-25\)	\(12\)	\(-\)	\(q+7q^{2}+9q^{3}+17q^{4}-5^{2}q^{5}+63q^{6}+\cdots\)
15.6.a.c	\(2\)	\(2.406\)	\(\Q(\sqrt{409}) \)	None	\(-1\)	\(-18\)	\(50\)	\(-112\)	\(-\)	\(q-\beta q^{2}-9q^{3}+(70+\beta )q^{4}+5^{2}q^{5}+\cdots\)
15.6.b.a	\(4\)	\(2.406\)	\(\Q(i, \sqrt{89})\)	None	\(0\)	\(0\)	\(120\)	\(0\)		\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-11+\beta _{3})q^{4}+\cdots\)
15.6.e.a	\(16\)	\(2.406\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-80\)		\(q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-13\beta _{3}-\beta _{6})q^{4}+\cdots\)
15.7.c.a	\(8\)	\(3.451\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(20\)	\(0\)	\(160\)		\(q-\beta _{2}q^{2}+(2-\beta _{5})q^{3}+(-41-\beta _{3}+\cdots)q^{4}+\cdots\)
15.7.d.a	\(1\)	\(3.451\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(-11\)	\(-27\)	\(125\)	\(0\)		\(q-11q^{2}-3^{3}q^{3}+57q^{4}+5^{3}q^{5}+\cdots\)
15.7.d.b	\(1\)	\(3.451\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(11\)	\(27\)	\(-125\)	\(0\)		\(q+11q^{2}+3^{3}q^{3}+57q^{4}-5^{3}q^{5}+\cdots\)
15.7.d.c	\(8\)	\(3.451\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{5}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots\)
15.7.f.a	\(12\)	\(3.451\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(16\)	\(0\)	\(136\)	\(-696\)		\(q+(1+\beta _{1}-\beta _{4})q^{2}-\beta _{6}q^{3}+(18\beta _{1}+\cdots)q^{4}+\cdots\)
15.8.a.a	\(1\)	\(4.686\)	\(\Q\)	None	\(-22\)	\(27\)	\(-125\)	\(-420\)	\(-\)	\(q-22q^{2}+3^{3}q^{3}+356q^{4}-5^{3}q^{5}+\cdots\)
15.8.a.b	\(1\)	\(4.686\)	\(\Q\)	None	\(-13\)	\(-27\)	\(-125\)	\(1380\)	\(+\)	\(q-13q^{2}-3^{3}q^{3}+41q^{4}-5^{3}q^{5}+\cdots\)
15.8.a.c	\(2\)	\(4.686\)	\(\Q(\sqrt{601}) \)	None	\(7\)	\(54\)	\(250\)	\(1304\)	\(+\)	\(q+(4-\beta )q^{2}+3^{3}q^{3}+(38-7\beta )q^{4}+\cdots\)
15.8.b.a	\(8\)	\(4.686\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(0\)	\(0\)	\(-444\)	\(0\)		\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-83-\beta _{4})q^{4}+\cdots\)
15.8.e.a	\(24\)	\(4.686\)		None	\(0\)	\(24\)	\(0\)	\(1344\)
15.9.c.a	\(10\)	\(6.111\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(-112\)	\(0\)	\(7156\)		\(q-\beta _{1}q^{2}+(-11-2\beta _{1}-\beta _{2})q^{3}+(-79+\cdots)q^{4}+\cdots\)
15.9.d.a	\(1\)	\(6.111\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(-17\)	\(-81\)	\(-625\)	\(0\)		\(q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots\)
15.9.d.b	\(1\)	\(6.111\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(17\)	\(81\)	\(625\)	\(0\)		\(q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots\)
15.9.d.c	\(12\)	\(6.111\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots\)
15.9.f.a	\(16\)	\(6.111\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(0\)	\(-444\)	\(4540\)		\(q+\beta _{2}q^{2}-\beta _{6}q^{3}+(158\beta _{1}-3\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)
15.10.a.a	\(1\)	\(7.726\)	\(\Q\)	None	\(-4\)	\(81\)	\(625\)	\(-7680\)	\(+\)	\(q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots\)
15.10.a.b	\(1\)	\(7.726\)	\(\Q\)	None	\(22\)	\(-81\)	\(-625\)	\(-5988\)	\(+\)	\(q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots\)
15.10.a.c	\(2\)	\(7.726\)	\(\Q(\sqrt{4729}) \)	None	\(19\)	\(162\)	\(-1250\)	\(-11872\)	\(-\)	\(q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots\)
15.10.a.d	\(2\)	\(7.726\)	\(\Q(\sqrt{241}) \)	None	\(31\)	\(-162\)	\(1250\)	\(14112\)	\(-\)	\(q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots\)
15.10.b.a	\(8\)	\(7.726\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(0\)	\(0\)	\(-690\)	\(0\)		\(q-\beta _{3}q^{2}+\beta _{4}q^{3}+(-149-\beta _{1})q^{4}+\cdots\)
15.10.e.a	\(32\)	\(7.726\)		None	\(0\)	\(-150\)	\(0\)	\(-9760\)
15.11.c.a	\(14\)	\(9.530\)	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None	\(0\)	\(44\)	\(0\)	\(-50548\)		\(q-\beta _{2}q^{2}+(3+\beta _{2}-\beta _{3})q^{3}+(-629+\cdots)q^{4}+\cdots\)
15.11.d.a	\(1\)	\(9.530\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(-61\)	\(243\)	\(-3125\)	\(0\)		\(q-61q^{2}+3^{5}q^{3}+2697q^{4}-5^{5}q^{5}+\cdots\)
15.11.d.b	\(1\)	\(9.530\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(61\)	\(-243\)	\(3125\)	\(0\)		\(q+61q^{2}-3^{5}q^{3}+2697q^{4}+5^{5}q^{5}+\cdots\)
15.11.d.c	\(16\)	\(9.530\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{6}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(137-\beta _{2}+\cdots)q^{4}+\cdots\)
15.11.f.a	\(20\)	\(9.530\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(-64\)	\(0\)	\(10676\)	\(10604\)		\(q+(-3-3\beta _{2}-\beta _{3})q^{2}+\beta _{6}q^{3}+(451\beta _{2}+\cdots)q^{4}+\cdots\)
15.12.a.a	\(1\)	\(11.525\)	\(\Q\)	None	\(-56\)	\(-243\)	\(3125\)	\(27984\)	\(-\)	\(q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots\)
15.12.a.b	\(2\)	\(11.525\)	\(\Q(\sqrt{1609}) \)	None	\(-22\)	\(486\)	\(-6250\)	\(-10864\)	\(-\)	\(q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots\)
15.12.a.c	\(2\)	\(11.525\)	\(\Q(\sqrt{1801}) \)	None	\(-13\)	\(-486\)	\(-6250\)	\(7784\)	\(+\)	\(q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots\)
15.12.a.d	\(3\)	\(11.525\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-1\)	\(729\)	\(9375\)	\(-14608\)	\(+\)	\(q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots\)
15.12.b.a	\(12\)	\(11.525\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(2556\)	\(0\)		\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots\)

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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.