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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 249 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$ -expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$ -expansion
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	$\Q(\sqrt{-3})$	None		✓	✓	✓	18.2.c.a	$2$	$0$	$-1$	$-3$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
18.3.b.a	$18$	$3$	18.b	3.b	$2$	$2$	$2$	$0.490$	$\Q(\sqrt{-2})$	None		✓	✓	✓	18.3.b.a	$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots$
18.3.d.a	$18$	$3$	18.d	9.d	$6$	$4$	$2$	$0.490$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓	✓	✓	18.3.d.a	$2$	$0$	$0$	$0$	$-18$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots$
18.4.a.a	$18$	$4$	18.a	1.a	$1$	$1$	$1$	$1.062$	$\Q$	None	✓		✓	✓	6.4.a.a	$1$	$0$	$2$	$0$	$-6$	$-16$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots$
18.4.c.a	$18$	$4$	18.c	9.c	$3$	$2$	$1$	$1.062$	$\Q(\sqrt{-3})$	None		✓			18.4.c.a	$2$	$0$	$-2$	$0$	$9$	$31$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
18.4.c.b	$18$	$4$	18.c	9.c	$3$	$4$	$2$	$1.062$	$\Q(\sqrt{-3}, \sqrt{-35})$	None		✓	✓		18.4.c.b	$2$	$0$	$4$	$3$	$9$	$-19$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots$
18.5.d.a	$18$	$5$	18.d	9.d	$6$	$8$	$4$	$1.861$	8.0. $\cdots$ .4	None		✓	✓	✓	18.5.d.a	$2$	$0$	$0$	$6$	$18$	$-26$		$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(2+\beta _{1}-3\beta _{2}-\beta _{5})q^{3}+\cdots$
18.6.a.a	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	$\Q$	None	✓	✓	✓	✓	18.6.a.a	$1$	$1$	$-4$	$0$	$-96$	$-148$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+2^{4}q^{4}-96q^{5}-148q^{7}+\cdots$
18.6.a.b	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	$\Q$	None	✓		✓	✓	6.6.a.a	$1$	$0$	$-4$	$0$	$66$	$176$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+2^{4}q^{4}+66q^{5}+176q^{7}+\cdots$
18.6.a.c	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	$\Q$	None	✓	✓	✓	✓	18.6.a.a	$1$	$0$	$4$	$0$	$96$	$-148$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+2^{4}q^{4}+96q^{5}-148q^{7}+\cdots$
18.6.c.a	$18$	$6$	18.c	9.c	$3$	$4$	$2$	$2.887$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			18.6.c.a	$2$	$0$	$8$	$0$	$-54$	$74$		$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+4\beta _{1}q^{2}+(-3+6\beta _{1}+\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$
18.6.c.b	$18$	$6$	18.c	9.c	$3$	$6$	$3$	$2.887$	6.0. $\cdots$ .3	None		✓	✓		18.6.c.b	$2$	$0$	$-12$	$9$	$-54$	$-132$		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-4\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$
18.7.b.a	$18$	$7$	18.b	3.b	$2$	$2$	$2$	$4.141$	$\Q(\sqrt{-2})$	None		✓	✓	✓	18.7.b.a	$2$	$0$	$0$	$0$	$0$	$-968$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4\beta q^{2}-2^{5}q^{4}+123\beta q^{5}-22^{2}q^{7}+\cdots$
18.7.d.a	$18$	$7$	18.d	9.d	$6$	$12$	$6$	$4.141$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	18.7.d.a	$2$	$0$	$0$	$-42$	$432$	$240$		$2^{10}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(-6+4\beta _{1}+\beta _{2}-\beta _{3}+\beta _{7}+\cdots)q^{3}+\cdots$
18.8.a.a	$18$	$8$	18.a	1.a	$1$	$1$	$1$	$5.623$	$\Q$	None	✓		✓	✓	6.8.a.a	$1$	$1$	$-8$	$0$	$114$	$-1576$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}+2^{6}q^{4}+114q^{5}-1576q^{7}+\cdots$
18.8.a.b	$18$	$8$	18.a	1.a	$1$	$1$	$1$	$5.623$	$\Q$	None	✓		✓	✓	2.8.a.a	$1$	$0$	$8$	$0$	$210$	$1016$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}+2^{6}q^{4}+210q^{5}+1016q^{7}+\cdots$
18.8.c.a	$18$	$8$	18.c	9.c	$3$	$6$	$3$	$5.623$	6.0. $\cdots$ .1	None		✓			18.8.c.a	$2$	$0$	$-24$	$-27$	$54$	$210$		$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q-8\beta _{1}q^{2}+(-14+19\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots$
18.8.c.b	$18$	$8$	18.c	9.c	$3$	$8$	$4$	$5.623$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓		18.8.c.b	$2$	$0$	$32$	$-12$	$54$	$-44$		$2^{4}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{3}]$	$q+(8-8\beta _{1})q^{2}+(-7+11\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots$
18.9.b.a	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	$\Q(\sqrt{-2})$	None		✓			18.9.b.a	$2$	$0$	$0$	$0$	$0$	$-7064$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8\beta q^{2}-2^{7}q^{4}+165\beta q^{5}-3532q^{7}+\cdots$
18.9.b.b	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	$\Q(\sqrt{-2})$	None		✓			18.9.b.b	$2$	$0$	$0$	$0$	$0$	$3304$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8\beta q^{2}-2^{7}q^{4}-645\beta q^{5}+1652q^{7}+\cdots$
18.9.d.a	$18$	$9$	18.d	9.d	$6$	$16$	$8$	$7.333$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	18.9.d.a	$2$	$0$	$0$	$126$	$-882$	$-1846$		$2^{28}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}+(7+2\beta _{1}+\beta _{3}+\beta _{4})q^{3}+\cdots$
18.10.a.a	$18$	$10$	18.a	1.a	$1$	$1$	$1$	$9.271$	$\Q$	None	✓		✓	✓	2.10.a.a	$1$	$0$	$-16$	$0$	$-870$	$-952$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+2^{8}q^{4}-870q^{5}-952q^{7}+\cdots$
18.10.a.b	$18$	$10$	18.a	1.a	$1$	$1$	$1$	$9.271$	$\Q$	None	✓	✓	✓	✓	18.10.a.b	$1$	$1$	$-16$	$0$	$-384$	$5852$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+2^{8}q^{4}-384q^{5}+5852q^{7}+\cdots$
18.10.a.c	$18$	$10$	18.a	1.a	$1$	$1$	$1$	$9.271$	$\Q$	None	✓		✓	✓	6.10.a.a	$1$	$1$	$16$	$0$	$-2694$	$-3544$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+2^{8}q^{4}-2694q^{5}-3544q^{7}+\cdots$
18.10.a.d	$18$	$10$	18.a	1.a	$1$	$1$	$1$	$9.271$	$\Q$	None	✓	✓	✓	✓	18.10.a.b	$1$	$0$	$16$	$0$	$384$	$5852$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+2^{8}q^{4}+384q^{5}+5852q^{7}+\cdots$
18.10.c.a	$18$	$10$	18.c	9.c	$3$	$8$	$4$	$9.271$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			18.10.c.a	$2$	$0$	$64$	$-81$	$171$	$7135$		$2^{6}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2^{4}-2^{4}\beta _{1})q^{2}+(-21+22\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
18.10.c.b	$18$	$10$	18.c	9.c	$3$	$10$	$5$	$9.271$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓	✓		18.10.c.b	$2$	$0$	$-80$	$156$	$171$	$-6451$		$2^{8}\cdot 3^{16}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-2^{4}\beta _{1}q^{2}+(29-3^{3}\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
18.11.b.a	$18$	$11$	18.b	3.b	$2$	$2$	$2$	$11.436$	$\Q(\sqrt{-2})$	None		✓	✓	✓	18.11.b.a	$2$	$0$	$0$	$0$	$0$	$41272$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2^{4}\beta q^{2}-2^{9}q^{4}-1443\beta q^{5}+20636q^{7}+\cdots$
18.11.d.a	$18$	$11$	18.d	9.d	$6$	$20$	$10$	$11.436$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	18.11.d.a	$2$	$0$	$0$	$-84$	$-9918$	$12238$		$2^{46}\cdot 3^{37}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(-2-4\beta _{1}+\beta _{3}-\beta _{4})q^{3}+\cdots$
18.12.a.a	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	$\Q$	None	✓		✓	✓	6.12.a.c	$1$	$1$	$-32$	$0$	$-3630$	$32936$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}+2^{10}q^{4}-3630q^{5}+32936q^{7}+\cdots$
18.12.a.b	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	$\Q$	None	✓	✓	✓	✓	18.12.a.b	$1$	$0$	$-32$	$0$	$5280$	$-49036$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}+2^{10}q^{4}+5280q^{5}-49036q^{7}+\cdots$
18.12.a.c	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	$\Q$	None	✓				6.12.a.a	$1$	$0$	$32$	$0$	$-5766$	$72464$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}+2^{10}q^{4}-5766q^{5}+72464q^{7}+\cdots$
18.12.a.d	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	$\Q$	None	✓	✓	✓	✓	18.12.a.b	$1$	$1$	$32$	$0$	$-5280$	$-49036$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}+2^{10}q^{4}-5280q^{5}-49036q^{7}+\cdots$
18.12.a.e	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	$\Q$	None	✓				6.12.a.b	$1$	$0$	$32$	$0$	$11730$	$-50008$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}+2^{10}q^{4}+11730q^{5}-50008q^{7}+\cdots$
18.12.c.a	$18$	$12$	18.c	9.c	$3$	$10$	$5$	$13.830$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓			18.12.c.a	$2$	$0$	$-160$	$-243$	$4104$	$44528$		$2^{12}\cdot 3^{21}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+2^{5}\beta _{1}q^{2}+(-55-62\beta _{1}+\beta _{5})q^{3}+\cdots$
18.12.c.b	$18$	$12$	18.c	9.c	$3$	$12$	$6$	$13.830$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		18.12.c.b	$2$	$0$	$192$	$0$	$4104$	$-61554$		$2^{14}\cdot 3^{25}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-2^{5}\beta _{1}q^{2}+(-39-77\beta _{1}-\beta _{3})q^{3}+\cdots$
18.13.b.a	$18$	$13$	18.b	3.b	$2$	$2$	$2$	$16.452$	$\Q(\sqrt{-2})$	None		✓			18.13.b.a	$2$	$0$	$0$	$0$	$0$	$-98744$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2^{5}\beta q^{2}-2^{11}q^{4}+795\beta q^{5}-49372q^{7}+\cdots$
18.13.b.b	$18$	$13$	18.b	3.b	$2$	$2$	$2$	$16.452$	$\Q(\sqrt{-2})$	None		✓			18.13.b.b	$2$	$0$	$0$	$0$	$0$	$67144$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2^{5}\beta q^{2}-2^{11}q^{4}+14565\beta q^{5}+\cdots$
18.13.d.a	$18$	$13$	18.d	9.d	$6$	$24$	$12$	$16.452$		None		✓	✓	✓	18.13.d.a	$2$	$0$	$0$	$-780$	$31968$	$-68640$			$\mathrm{SU}(2)[C_{6}]$
18.14.a.a	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	$\Q$	None	✓				6.14.a.a	$1$	$0$	$-64$	$0$	$-54654$	$176336$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}+2^{12}q^{4}-54654q^{5}+176336q^{7}+\cdots$
18.14.a.b	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	$\Q$	None	✓	✓	✓	✓	18.14.a.b	$1$	$1$	$-64$	$0$	$-15936$	$98252$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}+2^{12}q^{4}-15936q^{5}+98252q^{7}+\cdots$
18.14.a.c	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	$\Q$	None	✓				2.14.a.b	$1$	$0$	$-64$	$0$	$57450$	$64232$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}+2^{12}q^{4}+57450q^{5}+64232q^{7}+\cdots$
18.14.a.d	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	$\Q$	None	✓		✓	✓	2.14.a.a	$1$	$1$	$64$	$0$	$-3990$	$-433432$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{6}q^{2}+2^{12}q^{4}-3990q^{5}-433432q^{7}+\cdots$
18.14.a.e	$18$	$14$	18.a	1.a	$1$	$1$	$1$	$19.302$	$\Q$	None	✓	✓	✓	✓	18.14.a.b	$1$	$0$	$64$	$0$	$15936$	$98252$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{6}q^{2}+2^{12}q^{4}+15936q^{5}+98252q^{7}+\cdots$
18.14.c.a	$18$	$14$	18.c	9.c	$3$	$12$	$6$	$19.302$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			18.14.c.a	$2$	$0$	$384$	$1836$	$-36504$	$153942$		$2^{16}\cdot 3^{31}$	$\mathrm{SU}(2)[C_{3}]$	$q+2^{6}\beta _{1}q^{2}+(191-76\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$
18.14.c.b	$18$	$14$	18.c	9.c	$3$	$14$	$7$	$19.302$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓	✓		18.14.c.b	$2$	$0$	$-448$	$-507$	$-36504$	$33880$		$2^{26}\cdot 3^{37}$	$\mathrm{SU}(2)[C_{3}]$	$q-2^{6}\beta _{1}q^{2}+(7-87\beta _{1}-\beta _{4})q^{3}+(-2^{12}+\cdots)q^{4}+\cdots$
18.15.b.a	$18$	$15$	18.b	3.b	$2$	$2$	$2$	$22.379$	$\Q(\sqrt{-2})$	None		✓			18.15.b.a	$2$	$0$	$0$	$0$	$0$	$-522152$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2^{6}\beta q^{2}-2^{13}q^{4}+9075\beta q^{5}-261076q^{7}+\cdots$
18.15.b.b	$18$	$15$	18.b	3.b	$2$	$4$	$4$	$22.379$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None		✓	✓		18.15.b.b	$2$	$0$	$0$	$0$	$0$	$2659664$		$2^{7}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+2^{6}\beta _{1}q^{2}-2^{13}q^{4}+(-3081\beta _{1}+\cdots)q^{5}+\cdots$
18.15.d.a	$18$	$15$	18.d	9.d	$6$	$28$	$14$	$22.379$		None		✓	✓	✓	18.15.d.a	$2$	$0$	$0$	$3276$	$215982$	$292658$			$\mathrm{SU}(2)[C_{6}]$
18.16.a.a	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	$\Q$	None	✓				6.16.a.c	$1$	$1$	$-128$	$0$	$-77646$	$762104$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{7}q^{2}+2^{14}q^{4}-77646q^{5}+762104q^{7}+\cdots$

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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.