LMFDB - Newform search results

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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 334 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
10.3.c.a	$10$	$3$	10.c	5.c	$4$	$2$	$1$	$0.272$	$\Q(\sqrt{-1})$	None		✓	✓	✓	10.3.c.a	$2$	$0$	$-2$	$-4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+(2 i-2)q^{3}+2 i q^{4}+\cdots$
10.4.a.a	$10$	$4$	10.a	1.a	$1$	$1$	$1$	$0.590$	$\Q$	None	✓	✓	✓	✓	10.4.a.a	$1$	$0$	$2$	$-8$	$5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots$
10.4.b.a	$10$	$4$	10.b	5.b	$2$	$2$	$2$	$0.590$	$\Q(\sqrt{-1})$	None		✓	✓	✓	10.4.b.a	$2$	$0$	$0$	$0$	$-10$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-\beta q^{3}-4 q^{4}+(-5\beta-5)q^{5}+\cdots$
10.5.c.a	$10$	$5$	10.c	5.c	$4$	$2$	$1$	$1.034$	$\Q(\sqrt{-1})$	None		✓			10.5.c.a	$2$	$0$	$-4$	$18$	$-30$	$58$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i-2)q^{2}+(-9 i+9)q^{3}+\cdots$
10.5.c.b	$10$	$5$	10.c	5.c	$4$	$2$	$1$	$1.034$	$\Q(\sqrt{-1})$	None		✓			10.5.c.b	$2$	$0$	$4$	$2$	$-30$	$-38$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i+2)q^{2}+(-i+1)q^{3}+8 i q^{4}+\cdots$
10.6.a.a	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	$\Q$	None	✓	✓	✓	✓	10.6.a.a	$1$	$1$	$-4$	$-26$	$-25$	$-22$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-26q^{3}+2^{4}q^{4}-5^{2}q^{5}+104q^{6}+\cdots$
10.6.a.b	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	$\Q$	None	✓	✓	✓	✓	10.6.a.b	$1$	$0$	$-4$	$24$	$25$	$-172$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+24q^{3}+2^{4}q^{4}+5^{2}q^{5}-96q^{6}+\cdots$
10.6.a.c	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	$\Q$	None	✓	✓	✓	✓	10.6.a.c	$1$	$0$	$4$	$6$	$-25$	$-118$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+6q^{3}+2^{4}q^{4}-5^{2}q^{5}+24q^{6}+\cdots$
10.6.b.a	$10$	$6$	10.b	5.b	$2$	$2$	$2$	$1.604$	$\Q(\sqrt{-1})$	None		✓	✓	✓	10.6.b.a	$2$	$0$	$0$	$0$	$110$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{2}+7\beta q^{3}-16 q^{4}+(5\beta+55)q^{5}+\cdots$
10.7.c.a	$10$	$7$	10.c	5.c	$4$	$2$	$1$	$2.301$	$\Q(\sqrt{-1})$	None		✓			10.7.c.a	$2$	$0$	$-8$	$-46$	$-150$	$-494$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-4 i-4)q^{2}+(23 i-23)q^{3}+\cdots$
10.7.c.b	$10$	$7$	10.c	5.c	$4$	$4$	$2$	$2.301$	$\Q(i, \sqrt{129})$	None		✓	✓		10.7.c.b	$2$	$0$	$16$	$-18$	$330$	$-202$		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(4+4\beta _{1})q^{2}+(-5+4\beta _{1}-\beta _{3})q^{3}+\cdots$
10.8.a.a	$10$	$8$	10.a	1.a	$1$	$1$	$1$	$3.124$	$\Q$	None	✓	✓	✓	✓	10.8.a.a	$1$	$0$	$8$	$28$	$125$	$104$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}+28q^{3}+2^{6}q^{4}+5^{3}q^{5}+224q^{6}+\cdots$
10.8.b.a	$10$	$8$	10.b	5.b	$2$	$4$	$4$	$3.124$	$\Q(i, \sqrt{31})$	None		✓	✓	✓	10.8.b.a	$2$	$0$	$0$	$0$	$60$	$0$		$2^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(3\beta _{1}-\beta _{3})q^{3}-2^{6}q^{4}+(15+\cdots)q^{5}+\cdots$
10.9.c.a	$10$	$9$	10.c	5.c	$4$	$4$	$2$	$4.074$	$\Q(i, \sqrt{249})$	None		✓			10.9.c.a	$2$	$0$	$-32$	$54$	$90$	$-1186$		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
10.9.c.b	$10$	$9$	10.c	5.c	$4$	$4$	$2$	$4.074$	$\Q(i, \sqrt{601})$	None		✓			10.9.c.b	$2$	$0$	$32$	$86$	$-870$	$5726$		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots$
10.10.a.a	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓	✓	✓	10.10.a.a	$1$	$0$	$-16$	$-204$	$625$	$5432$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}-204q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
10.10.a.b	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓	✓	✓	10.10.a.b	$1$	$1$	$-16$	$46$	$-625$	$-10318$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+46q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots$
10.10.a.c	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓	✓	✓	10.10.a.c	$1$	$0$	$16$	$174$	$-625$	$4658$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+174q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots$
10.10.b.a	$10$	$10$	10.b	5.b	$2$	$4$	$4$	$5.150$	$\Q(i, \sqrt{319})$	None		✓	✓	✓	10.10.b.a	$2$	$0$	$0$	$0$	$-2580$	$0$		$2^{10}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-5\beta _{1}-\beta _{3})q^{3}-2^{8}q^{4}+\cdots$
10.11.c.a	$10$	$11$	10.c	5.c	$4$	$2$	$1$	$6.354$	$\Q(\sqrt{-1})$	None		✓			10.11.c.a	$2$	$0$	$32$	$-366$	$-3750$	$-16814$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(16 i+16)q^{2}+(183 i-183)q^{3}+\cdots$
10.11.c.b	$10$	$11$	10.c	5.c	$4$	$2$	$1$	$6.354$	$\Q(\sqrt{-1})$	None		✓			10.11.c.b	$2$	$0$	$32$	$114$	$5850$	$13906$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(16 i+16)q^{2}+(-57 i+57)q^{3}+\cdots$
10.11.c.c	$10$	$11$	10.c	5.c	$4$	$6$	$3$	$6.354$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		✓	✓		10.11.c.c	$2$	$0$	$-96$	$128$	$5460$	$13512$		$2^{8}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2^{4}-2^{4}\beta _{1})q^{2}+(21-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
10.12.a.a	$10$	$12$	10.a	1.a	$1$	$1$	$1$	$7.683$	$\Q$	None	✓	✓	✓	✓	10.12.a.a	$1$	$1$	$-32$	$-12$	$3125$	$-14176$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}-12q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots$
10.12.a.b	$10$	$12$	10.a	1.a	$1$	$1$	$1$	$7.683$	$\Q$	None	✓	✓	✓	✓	10.12.a.b	$1$	$0$	$-32$	$738$	$-3125$	$25574$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}+738q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$
10.12.a.c	$10$	$12$	10.a	1.a	$1$	$1$	$1$	$7.683$	$\Q$	None	✓	✓	✓	✓	10.12.a.c	$1$	$1$	$32$	$-318$	$-3125$	$-70714$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}-318q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$
10.12.a.d	$10$	$12$	10.a	1.a	$1$	$2$	$2$	$7.683$	$\Q(\sqrt{1969})$	None	✓	✓	✓	✓	10.12.a.d	$1$	$0$	$64$	$604$	$6250$	$14092$	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}+(302-\beta )q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots$
10.12.b.a	$10$	$12$	10.b	5.b	$2$	$6$	$6$	$7.683$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		✓	✓	✓	10.12.b.a	$2$	$0$	$0$	$0$	$530$	$0$		$2^{19}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{1}+3\beta _{2})q^{3}-2^{10}q^{4}+\cdots$
10.13.c.a	$10$	$13$	10.c	5.c	$4$	$6$	$3$	$9.140$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓			10.13.c.a	$2$	$0$	$-192$	$-936$	$-16260$	$-45336$		$2^{5}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2^{5}-2^{5}\beta _{1})q^{2}+(-156+156\beta _{1}+\cdots)q^{3}+\cdots$
10.13.c.b	$10$	$13$	10.c	5.c	$4$	$6$	$3$	$9.140$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓			10.13.c.b	$2$	$0$	$192$	$296$	$14460$	$-322104$		$2^{5}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2^{5}+2^{5}\beta _{1})q^{2}+(7^{2}-7^{2}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
10.14.a.a	$10$	$14$	10.a	1.a	$1$	$1$	$1$	$10.723$	$\Q$	None	✓	✓	✓	✓	10.14.a.a	$1$	$1$	$-64$	$-26$	$-15625$	$538538$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}-26q^{3}+2^{12}q^{4}-5^{6}q^{5}+\cdots$
10.14.a.b	$10$	$14$	10.a	1.a	$1$	$1$	$1$	$10.723$	$\Q$	None	✓	✓	✓	✓	10.14.a.b	$1$	$0$	$-64$	$1224$	$15625$	$-65212$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}+1224q^{3}+2^{12}q^{4}+5^{6}q^{5}+\cdots$
10.14.a.c	$10$	$14$	10.a	1.a	$1$	$1$	$1$	$10.723$	$\Q$	None	✓	✓	✓	✓	10.14.a.c	$1$	$0$	$64$	$-2394$	$-15625$	$438122$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{6}q^{2}-2394q^{3}+2^{12}q^{4}-5^{6}q^{5}+\cdots$
10.14.b.a	$10$	$14$	10.b	5.b	$2$	$6$	$6$	$10.723$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		✓	✓	✓	10.14.b.a	$2$	$0$	$0$	$0$	$-2470$	$0$		$2^{21}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}-2^{12}q^{4}+(-412+\cdots)q^{5}+\cdots$
10.15.c.a	$10$	$15$	10.c	5.c	$4$	$6$	$3$	$12.433$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		✓			10.15.c.a	$2$	$0$	$-384$	$2912$	$82500$	$943128$		$2^{7}\cdot 3^{2}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2^{6}+2^{6}\beta _{1})q^{2}+(485+485\beta _{1}+\cdots)q^{3}+\cdots$
10.15.c.b	$10$	$15$	10.c	5.c	$4$	$8$	$4$	$12.433$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓		10.15.c.b	$2$	$0$	$512$	$1404$	$-100860$	$1333276$		$2^{14}\cdot 3^{4}\cdot 5^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2^{6}-2^{6}\beta _{1})q^{2}+(175+176\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots$
10.16.a.a	$10$	$16$	10.a	1.a	$1$	$1$	$1$	$14.269$	$\Q$	None	✓	✓	✓	✓	10.16.a.a	$1$	$1$	$-128$	$-5568$	$78125$	$2564996$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{7}q^{2}-5568q^{3}+2^{14}q^{4}+5^{7}q^{5}+\cdots$
10.16.a.b	$10$	$16$	10.a	1.a	$1$	$1$	$1$	$14.269$	$\Q$	None	✓	✓	✓	✓	10.16.a.b	$1$	$0$	$-128$	$-918$	$-78125$	$-953554$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{7}q^{2}-918q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots$
10.16.a.c	$10$	$16$	10.a	1.a	$1$	$1$	$1$	$14.269$	$\Q$	None	✓	✓	✓	✓	10.16.a.c	$1$	$1$	$128$	$-1302$	$-78125$	$-90706$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{7}q^{2}-1302q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots$
10.16.a.d	$10$	$16$	10.a	1.a	$1$	$2$	$2$	$14.269$	$\Q(\sqrt{239569})$	None	✓	✓	✓	✓	10.16.a.d	$1$	$0$	$256$	$-1844$	$156250$	$-984932$	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q+2^{7}q^{2}+(-922-\beta )q^{3}+2^{14}q^{4}+\cdots$
10.16.b.a	$10$	$16$	10.b	5.b	$2$	$8$	$8$	$14.269$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓	✓	10.16.b.a	$2$	$0$	$0$	$0$	$251400$	$0$		$2^{38}\cdot 3^{2}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}-2^{14}q^{4}+(31425+\cdots)q^{5}+\cdots$
10.17.c.a	$10$	$17$	10.c	5.c	$4$	$8$	$4$	$16.232$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			10.17.c.a	$2$	$0$	$-1024$	$-5382$	$184830$	$-1586702$		$2^{13}\cdot 3^{8}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2^{7}+2^{7}\beta _{1})q^{2}+(-673-673\beta _{1}+\cdots)q^{3}+\cdots$
10.17.c.b	$10$	$17$	10.c	5.c	$4$	$8$	$4$	$16.232$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			10.17.c.b	$2$	$0$	$1024$	$-10438$	$-216450$	$3127282$		$2^{13}\cdot 3^{2}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2^{7}+2^{7}\beta _{1})q^{2}+(-1305+1305\beta _{1}+\cdots)q^{3}+\cdots$
10.18.a.a	$10$	$18$	10.a	1.a	$1$	$1$	$1$	$18.322$	$\Q$	None	✓	✓	✓	✓	10.18.a.a	$1$	$1$	$256$	$-14976$	$390625$	$14808668$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{8}q^{2}-14976q^{3}+2^{16}q^{4}+5^{8}q^{5}+\cdots$
10.18.a.b	$10$	$18$	10.a	1.a	$1$	$2$	$2$	$18.322$	$\Q(\sqrt{36061})$	None	✓	✓	✓	✓	10.18.a.b	$1$	$1$	$-512$	$-6308$	$-781250$	$6543844$	$+$	$2^{5}\cdot 5$	$\mathrm{SU}(2)$	$q-2^{8}q^{2}+(-3154-\beta )q^{3}+2^{16}q^{4}+\cdots$
10.18.a.c	$10$	$18$	10.a	1.a	$1$	$2$	$2$	$18.322$	$\Q(\sqrt{83281})$	None	✓	✓	✓	✓	10.18.a.c	$1$	$0$	$-512$	$-1308$	$781250$	$603844$	$-$	$2^{2}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	$q-2^{8}q^{2}+(-654-\beta )q^{3}+2^{16}q^{4}+\cdots$
10.18.a.d	$10$	$18$	10.a	1.a	$1$	$2$	$2$	$18.322$	$\Q(\sqrt{2941})$	None	✓	✓	✓	✓	10.18.a.d	$1$	$0$	$512$	$17628$	$-781250$	$27684196$	$-$	$2^{5}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	$q+2^{8}q^{2}+(8814-\beta )q^{3}+2^{16}q^{4}+\cdots$
10.18.b.a	$10$	$18$	10.b	5.b	$2$	$8$	$8$	$18.322$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓	✓	10.18.b.a	$2$	$0$	$0$	$0$	$-1225560$	$0$		$2^{40}\cdot 3^{4}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}-2^{16}q^{4}+\cdots$
10.19.c.a	$10$	$19$	10.c	5.c	$4$	$8$	$4$	$20.539$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			10.19.c.a	$2$	$0$	$2048$	$37026$	$-3132450$	$-43579766$		$2^{15}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2^{8}-2^{8}\beta _{1})q^{2}+(4628+4628\beta _{1}+\cdots)q^{3}+\cdots$
10.19.c.b	$10$	$19$	10.c	5.c	$4$	$10$	$5$	$20.539$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓	✓		10.19.c.b	$2$	$0$	$-2560$	$3230$	$-1436130$	$-71828530$		$2^{22}\cdot 3^{8}\cdot 5^{17}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2^{8}-2^{8}\beta _{1})q^{2}+(323-323\beta _{1}+\cdots)q^{3}+\cdots$
10.20.a.a	$10$	$20$	10.a	1.a	$1$	$1$	$1$	$22.882$	$\Q$	None	✓	✓	✓	✓	10.20.a.a	$1$	$0$	$-512$	$-26622$	$-1953125$	$-39884026$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{9}q^{2}-26622q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots$

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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.