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-twists	CM/RM discriminant	Inner twist count*	Is self-dual?	Analytic rank

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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
1.12.a.a	$1$	$0.768$	$\Q$	None	$-24$	$252$	$4830$	$-16744$	$+$	$q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}+\cdots$
2.10.a.a	$1$	$1.030$	$\Q$	None	$16$	$-156$	$870$	$-952$	$-$	$q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots$
3.9.b.a	$2$	$1.222$	$\Q(\sqrt{-14}) $	None	$0$	$90$	$0$	$-3500$		$q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots$
1.16.a.a	$1$	$1.427$	$\Q$	None	$216$	$-3348$	$52110$	$2822456$	$+$	$q+6^{3}q^{2}-3348q^{3}+13888q^{4}+52110q^{5}+\cdots$
3.10.a.a	$1$	$1.545$	$\Q$	None	$-36$	$-81$	$-1314$	$-4480$	$+$	$q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots$
3.10.a.b	$1$	$1.545$	$\Q$	None	$18$	$81$	$-1530$	$9128$	$-$	$q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots$
4.9.b.a	$1$	$1.630$	$\Q$	$\Q(\sqrt{-1}) $	$16$	$0$	$-1054$	$0$		$q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots$
4.9.b.b	$2$	$1.630$	$\Q(\sqrt{-39}) $	None	$-20$	$0$	$1220$	$0$		$q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots$
3.11.b.a	$2$	$1.906$	$\Q(\sqrt{-5}) $	None	$0$	$-54$	$0$	$34468$		$q+\beta q^{2}+(-3^{3}+9\beta )q^{3}+304q^{4}+\cdots$
5.9.c.a	$6$	$2.037$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-2$	$-72$	$220$	$-2352$		$q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots$
4.10.a.a	$1$	$2.060$	$\Q$	None	$0$	$228$	$-666$	$-6328$	$-$	$q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots$
2.14.a.a	$1$	$2.145$	$\Q$	None	$-64$	$-1836$	$3990$	$-433432$	$+$	$q-2^{6}q^{2}-1836q^{3}+2^{12}q^{4}+3990q^{5}+\cdots$
2.14.a.b	$1$	$2.145$	$\Q$	None	$64$	$1236$	$-57450$	$64232$	$-$	$q+2^{6}q^{2}+1236q^{3}+2^{12}q^{4}-57450q^{5}+\cdots$
3.12.a.a	$1$	$2.305$	$\Q$	None	$78$	$-243$	$-5370$	$-27760$	$+$	$q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots$
6.9.b.a	$2$	$2.444$	$\Q(\sqrt{-2}) $	None	$0$	$-126$	$0$	$5572$		$q+2\beta q^{2}+(-63+9\beta )q^{3}-2^{7}q^{4}+\cdots$
4.11.b.a	$4$	$2.541$	4.0.26777625.2	None	$-12$	$0$	$-1560$	$0$		$q+(-3+\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots$
5.10.a.a	$1$	$2.575$	$\Q$	None	$-8$	$-114$	$-625$	$4242$	$+$	$q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots$
5.10.a.b	$2$	$2.575$	$\Q(\sqrt{1009}) $	None	$-10$	$260$	$1250$	$1700$	$-$	$q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots$
5.10.b.a	$4$	$2.575$	4.0.49740556.1	None	$0$	$0$	$1140$	$0$		$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-342+\cdots)q^{4}+\cdots$
3.13.b.a	$1$	$2.742$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$729$	$0$	$-153502$		$q+3^{6}q^{3}+2^{12}q^{4}-153502q^{7}+3^{12}q^{9}+\cdots$
3.13.b.b	$2$	$2.742$	$\Q(\sqrt{-26}) $	None	$0$	$-1350$	$0$	$80500$		$q+\beta q^{2}+(-675-3\beta )q^{3}-4328q^{4}+\cdots$
7.9.b.a	$1$	$2.852$	$\Q$	$\Q(\sqrt{-7}) $	$-31$	$0$	$0$	$2401$		$q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots$
7.9.b.b	$4$	$2.852$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	None	$32$	$0$	$0$	$1428$		$q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots$
7.9.d.a	$8$	$2.852$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$-4$	$-84$	$-840$	$-140$		$q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots$
2.16.a.a	$1$	$2.854$	$\Q$	None	$-128$	$6252$	$90510$	$56$	$+$	$q-2^{7}q^{2}+6252q^{3}+2^{14}q^{4}+90510q^{5}+\cdots$
4.12.a.a	$1$	$3.073$	$\Q$	None	$0$	$-516$	$-10530$	$49304$	$-$	$q-516q^{3}-10530q^{5}+49304q^{7}+\cdots$
6.10.a.a	$1$	$3.090$	$\Q$	None	$-16$	$81$	$2694$	$-3544$	$-$	$q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+2694q^{5}+\cdots$
5.11.c.a	$8$	$3.177$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$30$	$60$	$-5340$	$-14500$		$q+(4+4\beta _{1}-\beta _{3})q^{2}+(8-8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
3.14.a.a	$1$	$3.217$	$\Q$	None	$-12$	$-729$	$-30210$	$235088$	$+$	$q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots$
3.14.a.b	$2$	$3.217$	$\Q(\sqrt{1969}) $	None	$-54$	$1458$	$40716$	$-21008$	$-$	$q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots$
8.9.d.a	$1$	$3.259$	$\Q$	$\Q(\sqrt{-2}) $	$16$	$34$	$0$	$0$		$q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots$
8.9.d.b	$6$	$3.259$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-14$	$-36$	$0$	$0$		$q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots$
7.10.a.a	$2$	$3.605$	$\Q(\sqrt{193}) $	None	$-6$	$-86$	$-2238$	$-4802$	$+$	$q+(-3-\beta )q^{2}+(-43+11\beta )q^{3}+(-310+\cdots)q^{4}+\cdots$
7.10.a.b	$3$	$3.605$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$21$	$84$	$1554$	$7203$	$-$	$q+(7-\beta _{2})q^{2}+(28-\beta _{1}-\beta _{2})q^{3}+(519+\cdots)q^{4}+\cdots$
7.10.c.a	$10$	$3.605$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-18$	$161$	$1533$	$-1036$		$q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots$
4.13.b.a	$1$	$3.656$	$\Q$	$\Q(\sqrt{-1}) $	$-64$	$0$	$23506$	$0$		$q-2^{6}q^{2}+2^{12}q^{4}+23506q^{5}-2^{18}q^{8}+\cdots$
4.13.b.b	$4$	$3.656$	4.0.8546467905.1	None	$108$	$0$	$-18360$	$0$		$q+(3^{3}+\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-380+\cdots)q^{4}+\cdots$
9.9.b.a	$2$	$3.666$	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$3304$		$q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots$
9.9.d.a	$14$	$3.666$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$-3$	$-93$	$438$	$922$		$q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots$
3.15.b.a	$4$	$3.730$	4.0.1929141760.2	None	$0$	$2196$	$0$	$825608$		$q+\beta _{1}q^{2}+(549+3\beta _{1}-\beta _{2})q^{3}+(-9824+\cdots)q^{4}+\cdots$
6.11.b.a	$4$	$3.812$	$\Q(\sqrt{-2}, \sqrt{85})$	None	$0$	$84$	$0$	$-45112$		$q+\beta _{1}q^{2}+(21-3\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots$
5.12.a.a	$1$	$3.842$	$\Q$	None	$34$	$-792$	$3125$	$-17556$	$-$	$q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots$
5.12.a.b	$2$	$3.842$	$\Q(\sqrt{151}) $	None	$-20$	$-220$	$-6250$	$57900$	$+$	$q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots$
5.12.b.a	$4$	$3.842$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$0$	$0$	$-300$	$0$		$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-18-\beta _{2})q^{4}+\cdots$
10.9.c.a	$4$	$4.074$	$\Q(i, \sqrt{249})$	None	$-32$	$54$	$90$	$-1186$		$q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
10.9.c.b	$4$	$4.074$	$\Q(i, \sqrt{601})$	None	$32$	$86$	$-870$	$5726$		$q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots$
8.10.a.a	$1$	$4.120$	$\Q$	None	$0$	$-60$	$-2074$	$-4344$	$+$	$q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots$
8.10.a.b	$1$	$4.120$	$\Q$	None	$0$	$68$	$1510$	$10248$	$-$	$q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots$
8.10.b.a	$8$	$4.120$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-18$	$0$	$0$	$4800$		$q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots$
3.16.a.a	$1$	$4.281$	$\Q$	None	$-234$	$-2187$	$280710$	$-1373344$	$+$	$q-234q^{2}-3^{7}q^{3}+21988q^{4}+280710q^{5}+\cdots$

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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
1.12.a.a	\(1\)	\(0.768\)	\(\Q\)	None	\(-24\)	\(252\)	\(4830\)	\(-16744\)	\(+\)	\(q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}+\cdots\)
2.10.a.a	\(1\)	\(1.030\)	\(\Q\)	None	\(16\)	\(-156\)	\(870\)	\(-952\)	\(-\)	\(q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots\)
3.9.b.a	\(2\)	\(1.222\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(90\)	\(0\)	\(-3500\)		\(q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots\)
1.16.a.a	\(1\)	\(1.427\)	\(\Q\)	None	\(216\)	\(-3348\)	\(52110\)	\(2822456\)	\(+\)	\(q+6^{3}q^{2}-3348q^{3}+13888q^{4}+52110q^{5}+\cdots\)
3.10.a.a	\(1\)	\(1.545\)	\(\Q\)	None	\(-36\)	\(-81\)	\(-1314\)	\(-4480\)	\(+\)	\(q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots\)
3.10.a.b	\(1\)	\(1.545\)	\(\Q\)	None	\(18\)	\(81\)	\(-1530\)	\(9128\)	\(-\)	\(q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots\)
4.9.b.a	\(1\)	\(1.630\)	\(\Q\)	\(\Q(\sqrt{-1}) \)	\(16\)	\(0\)	\(-1054\)	\(0\)		\(q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots\)
4.9.b.b	\(2\)	\(1.630\)	\(\Q(\sqrt{-39}) \)	None	\(-20\)	\(0\)	\(1220\)	\(0\)		\(q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots\)
3.11.b.a	\(2\)	\(1.906\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(-54\)	\(0\)	\(34468\)		\(q+\beta q^{2}+(-3^{3}+9\beta )q^{3}+304q^{4}+\cdots\)
5.9.c.a	\(6\)	\(2.037\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-2\)	\(-72\)	\(220\)	\(-2352\)		\(q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots\)
4.10.a.a	\(1\)	\(2.060\)	\(\Q\)	None	\(0\)	\(228\)	\(-666\)	\(-6328\)	\(-\)	\(q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots\)
2.14.a.a	\(1\)	\(2.145\)	\(\Q\)	None	\(-64\)	\(-1836\)	\(3990\)	\(-433432\)	\(+\)	\(q-2^{6}q^{2}-1836q^{3}+2^{12}q^{4}+3990q^{5}+\cdots\)
2.14.a.b	\(1\)	\(2.145\)	\(\Q\)	None	\(64\)	\(1236\)	\(-57450\)	\(64232\)	\(-\)	\(q+2^{6}q^{2}+1236q^{3}+2^{12}q^{4}-57450q^{5}+\cdots\)
3.12.a.a	\(1\)	\(2.305\)	\(\Q\)	None	\(78\)	\(-243\)	\(-5370\)	\(-27760\)	\(+\)	\(q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots\)
6.9.b.a	\(2\)	\(2.444\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(-126\)	\(0\)	\(5572\)		\(q+2\beta q^{2}+(-63+9\beta )q^{3}-2^{7}q^{4}+\cdots\)
4.11.b.a	\(4\)	\(2.541\)	4.0.26777625.2	None	\(-12\)	\(0\)	\(-1560\)	\(0\)		\(q+(-3+\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
5.10.a.a	\(1\)	\(2.575\)	\(\Q\)	None	\(-8\)	\(-114\)	\(-625\)	\(4242\)	\(+\)	\(q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots\)
5.10.a.b	\(2\)	\(2.575\)	\(\Q(\sqrt{1009}) \)	None	\(-10\)	\(260\)	\(1250\)	\(1700\)	\(-\)	\(q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)
5.10.b.a	\(4\)	\(2.575\)	4.0.49740556.1	None	\(0\)	\(0\)	\(1140\)	\(0\)		\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-342+\cdots)q^{4}+\cdots\)
3.13.b.a	\(1\)	\(2.742\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(729\)	\(0\)	\(-153502\)		\(q+3^{6}q^{3}+2^{12}q^{4}-153502q^{7}+3^{12}q^{9}+\cdots\)
3.13.b.b	\(2\)	\(2.742\)	\(\Q(\sqrt{-26}) \)	None	\(0\)	\(-1350\)	\(0\)	\(80500\)		\(q+\beta q^{2}+(-675-3\beta )q^{3}-4328q^{4}+\cdots\)
7.9.b.a	\(1\)	\(2.852\)	\(\Q\)	\(\Q(\sqrt{-7}) \)	\(-31\)	\(0\)	\(0\)	\(2401\)		\(q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots\)
7.9.b.b	\(4\)	\(2.852\)	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None	\(32\)	\(0\)	\(0\)	\(1428\)		\(q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots\)
7.9.d.a	\(8\)	\(2.852\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(-4\)	\(-84\)	\(-840\)	\(-140\)		\(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots\)
2.16.a.a	\(1\)	\(2.854\)	\(\Q\)	None	\(-128\)	\(6252\)	\(90510\)	\(56\)	\(+\)	\(q-2^{7}q^{2}+6252q^{3}+2^{14}q^{4}+90510q^{5}+\cdots\)
4.12.a.a	\(1\)	\(3.073\)	\(\Q\)	None	\(0\)	\(-516\)	\(-10530\)	\(49304\)	\(-\)	\(q-516q^{3}-10530q^{5}+49304q^{7}+\cdots\)
6.10.a.a	\(1\)	\(3.090\)	\(\Q\)	None	\(-16\)	\(81\)	\(2694\)	\(-3544\)	\(-\)	\(q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+2694q^{5}+\cdots\)
5.11.c.a	\(8\)	\(3.177\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(30\)	\(60\)	\(-5340\)	\(-14500\)		\(q+(4+4\beta _{1}-\beta _{3})q^{2}+(8-8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
3.14.a.a	\(1\)	\(3.217\)	\(\Q\)	None	\(-12\)	\(-729\)	\(-30210\)	\(235088\)	\(+\)	\(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\)
3.14.a.b	\(2\)	\(3.217\)	\(\Q(\sqrt{1969}) \)	None	\(-54\)	\(1458\)	\(40716\)	\(-21008\)	\(-\)	\(q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots\)
8.9.d.a	\(1\)	\(3.259\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(16\)	\(34\)	\(0\)	\(0\)		\(q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots\)
8.9.d.b	\(6\)	\(3.259\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-14\)	\(-36\)	\(0\)	\(0\)		\(q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots\)
7.10.a.a	\(2\)	\(3.605\)	\(\Q(\sqrt{193}) \)	None	\(-6\)	\(-86\)	\(-2238\)	\(-4802\)	\(+\)	\(q+(-3-\beta )q^{2}+(-43+11\beta )q^{3}+(-310+\cdots)q^{4}+\cdots\)
7.10.a.b	\(3\)	\(3.605\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(21\)	\(84\)	\(1554\)	\(7203\)	\(-\)	\(q+(7-\beta _{2})q^{2}+(28-\beta _{1}-\beta _{2})q^{3}+(519+\cdots)q^{4}+\cdots\)
7.10.c.a	\(10\)	\(3.605\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-18\)	\(161\)	\(1533\)	\(-1036\)		\(q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots\)
4.13.b.a	\(1\)	\(3.656\)	\(\Q\)	\(\Q(\sqrt{-1}) \)	\(-64\)	\(0\)	\(23506\)	\(0\)		\(q-2^{6}q^{2}+2^{12}q^{4}+23506q^{5}-2^{18}q^{8}+\cdots\)
4.13.b.b	\(4\)	\(3.656\)	4.0.8546467905.1	None	\(108\)	\(0\)	\(-18360\)	\(0\)		\(q+(3^{3}+\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-380+\cdots)q^{4}+\cdots\)
9.9.b.a	\(2\)	\(3.666\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(3304\)		\(q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots\)
9.9.d.a	\(14\)	\(3.666\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(-3\)	\(-93\)	\(438\)	\(922\)		\(q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots\)
3.15.b.a	\(4\)	\(3.730\)	4.0.1929141760.2	None	\(0\)	\(2196\)	\(0\)	\(825608\)		\(q+\beta _{1}q^{2}+(549+3\beta _{1}-\beta _{2})q^{3}+(-9824+\cdots)q^{4}+\cdots\)
6.11.b.a	\(4\)	\(3.812\)	\(\Q(\sqrt{-2}, \sqrt{85})\)	None	\(0\)	\(84\)	\(0\)	\(-45112\)		\(q+\beta _{1}q^{2}+(21-3\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
5.12.a.a	\(1\)	\(3.842\)	\(\Q\)	None	\(34\)	\(-792\)	\(3125\)	\(-17556\)	\(-\)	\(q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots\)
5.12.a.b	\(2\)	\(3.842\)	\(\Q(\sqrt{151}) \)	None	\(-20\)	\(-220\)	\(-6250\)	\(57900\)	\(+\)	\(q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots\)
5.12.b.a	\(4\)	\(3.842\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(0\)	\(0\)	\(-300\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-18-\beta _{2})q^{4}+\cdots\)
10.9.c.a	\(4\)	\(4.074\)	\(\Q(i, \sqrt{249})\)	None	\(-32\)	\(54\)	\(90\)	\(-1186\)		\(q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.9.c.b	\(4\)	\(4.074\)	\(\Q(i, \sqrt{601})\)	None	\(32\)	\(86\)	\(-870\)	\(5726\)		\(q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots\)
8.10.a.a	\(1\)	\(4.120\)	\(\Q\)	None	\(0\)	\(-60\)	\(-2074\)	\(-4344\)	\(+\)	\(q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots\)
8.10.a.b	\(1\)	\(4.120\)	\(\Q\)	None	\(0\)	\(68\)	\(1510\)	\(10248\)	\(-\)	\(q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots\)
8.10.b.a	\(8\)	\(4.120\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-18\)	\(0\)	\(0\)	\(4800\)		\(q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots\)
3.16.a.a	\(1\)	\(4.281\)	\(\Q\)	None	\(-234\)	\(-2187\)	\(280710\)	\(-1373344\)	\(+\)	\(q-234q^{2}-3^{7}q^{3}+21988q^{4}+280710q^{5}+\cdots\)

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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.