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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

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
32.2.a.a	$32$	$2$	32.a	1.a	$1$	$1$	$1$	$0.256$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots$
32.2.g.a	$32$	$2$	32.g	32.g	$8$	$4$	$1$	$0.256$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots$
32.2.g.b	$32$	$2$	32.g	32.g	$8$	$8$	$2$	$0.256$	8.0.18939904.2	None		$2$	$0$	$-4$	$-4$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots$
32.3.c.a	$32$	$3$	32.c	4.b	$2$	$2$	$2$	$0.872$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2q^{5}-2iq^{7}-7q^{9}-iq^{11}+\cdots$
32.3.d.a	$32$	$3$	32.d	8.d	$2$	$1$	$1$	$0.872$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{3}-5q^{9}-14q^{11}+2q^{17}+34q^{19}+\cdots$
32.3.h.a	$32$	$3$	32.h	32.h	$8$	$28$	$7$	$0.872$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
32.4.a.a	$32$	$4$	32.a	1.a	$1$	$1$	$1$	$1.888$	$\Q$	None	✓	$1$	$1$	$0$	$-8$	$-10$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}-10q^{5}-2^{4}q^{7}+37q^{9}+40q^{11}+\cdots$
32.4.a.b	$32$	$4$	32.a	1.a	$1$	$1$	$1$	$1.888$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$22$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+22q^{5}-3^{3}q^{9}-18q^{13}-94q^{17}+\cdots$
32.4.a.c	$32$	$4$	32.a	1.a	$1$	$1$	$1$	$1.888$	$\Q$	None	✓	$1$	$0$	$0$	$8$	$-10$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{3}-10q^{5}+2^{4}q^{7}+37q^{9}-40q^{11}+\cdots$
32.4.b.a	$32$	$4$	32.b	8.b	$2$	$2$	$2$	$1.888$	$\Q(\sqrt{-7}) $	None		$2$	$0$	$0$	$0$	$0$	$16$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-2\beta q^{5}+8q^{7}-q^{9}+3\beta q^{11}+\cdots$
32.4.g.a	$32$	$4$	32.g	32.g	$8$	$44$	$11$	$1.888$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
32.5.c.a	$32$	$5$	32.c	4.b	$2$	$2$	$2$	$3.308$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-76$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}-38q^{5}+2iq^{7}-63q^{9}+\cdots$
32.5.c.b	$32$	$5$	32.c	4.b	$2$	$2$	$2$	$3.308$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$52$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+26q^{5}+22iq^{7}+65q^{9}+\cdots$
32.5.d.a	$32$	$5$	32.d	8.d	$2$	$1$	$1$	$3.308$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$14$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+14q^{3}+115q^{9}+46q^{11}-574q^{17}+\cdots$
32.5.d.b	$32$	$5$	32.d	8.d	$2$	$2$	$2$	$3.308$	$\Q(\sqrt{-15}) $	None		$2$	$0$	$0$	$-12$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-6q^{3}-\beta q^{5}-2\beta q^{7}-45q^{9}+26q^{11}+\cdots$
32.5.h.a	$32$	$5$	32.h	32.h	$8$	$60$	$15$	$3.308$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
32.6.a.a	$32$	$6$	32.a	1.a	$1$	$1$	$1$	$5.132$	$\Q$	None	✓	$1$	$1$	$0$	$-8$	$14$	$-208$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}+14q^{5}-208q^{7}-179q^{9}+\cdots$
32.6.a.b	$32$	$6$	32.a	1.a	$1$	$1$	$1$	$5.132$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$-82$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-82q^{5}-3^{5}q^{9}-1194q^{13}+2242q^{17}+\cdots$
32.6.a.c	$32$	$6$	32.a	1.a	$1$	$1$	$1$	$5.132$	$\Q$	None	✓	$1$	$0$	$0$	$8$	$14$	$208$	$-$	$1$	$\mathrm{SU}(2)$	$q+8q^{3}+14q^{5}+208q^{7}-179q^{9}+\cdots$
32.6.a.d	$32$	$6$	32.a	1.a	$1$	$2$	$2$	$5.132$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$92$	$0$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta q^{3}+46q^{5}-6\beta q^{7}+525q^{9}+\cdots$
32.6.b.a	$32$	$6$	32.b	8.b	$2$	$4$	$4$	$5.132$	4.0.218489.1	None		$2$	$0$	$0$	$0$	$0$	$-96$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-24-\beta _{3})q^{7}+\cdots$
32.6.g.a	$32$	$6$	32.g	32.g	$8$	$76$	$19$	$5.132$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
32.7.c.a	$32$	$7$	32.c	4.b	$2$	$2$	$2$	$7.362$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$100$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+50q^{5}+46iq^{7}+713q^{9}+\cdots$
32.7.c.b	$32$	$7$	32.c	4.b	$2$	$4$	$4$	$7.362$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$0$	$0$	$-56$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-14-\beta _{3})q^{5}+(2\beta _{1}-5\beta _{2}+\cdots)q^{7}+\cdots$
32.7.d.a	$32$	$7$	32.d	8.d	$2$	$1$	$1$	$7.362$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$-46$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-46q^{3}+1387q^{9}+2338q^{11}-1726q^{17}+\cdots$
32.7.d.b	$32$	$7$	32.d	8.d	$2$	$4$	$4$	$7.362$	4.0.3803625.2	None		$2$	$0$	$0$	$48$	$0$	$0$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+(12-\beta _{1})q^{3}-\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots$
32.7.h.a	$32$	$7$	32.h	32.h	$8$	$92$	$23$	$7.362$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
32.8.a.a	$32$	$8$	32.a	1.a	$1$	$1$	$1$	$9.996$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$-58$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-58q^{5}-3^{7}q^{9}-8898q^{13}-40094q^{17}+\cdots$
32.8.a.b	$32$	$8$	32.a	1.a	$1$	$2$	$2$	$9.996$	$\Q(\sqrt{10}) $	None	✓	$1$	$0$	$0$	$-16$	$-180$	$1248$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-8+\beta )q^{3}+(-90+8\beta )q^{5}+(624+\cdots)q^{7}+\cdots$
32.8.a.c	$32$	$8$	32.a	1.a	$1$	$2$	$2$	$9.996$	$\Q(\sqrt{15}) $	None	✓	$2$	$0$	$0$	$0$	$140$	$0$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta q^{3}+70q^{5}+18\beta q^{7}+1653q^{9}+\cdots$
32.8.a.d	$32$	$8$	32.a	1.a	$1$	$2$	$2$	$9.996$	$\Q(\sqrt{10}) $	None	✓	$1$	$1$	$0$	$16$	$-180$	$-1248$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(8+\beta )q^{3}+(-90-8\beta )q^{5}+(-624+\cdots)q^{7}+\cdots$
32.8.b.a	$32$	$8$	32.b	8.b	$2$	$6$	$6$	$9.996$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$688$		$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(115+\beta _{1}+\cdots)q^{7}+\cdots$
32.8.g.a	$32$	$8$	32.g	32.g	$8$	$108$	$27$	$9.996$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
32.9.c.a	$32$	$9$	32.c	4.b	$2$	$4$	$4$	$13.036$	$\Q(i, \sqrt{39})$	None		$2$	$0$	$0$	$0$	$-728$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}+(-182+\beta _{2})q^{5}+(17\beta _{1}+\cdots)q^{7}+\cdots$
32.9.c.b	$32$	$9$	32.c	4.b	$2$	$4$	$4$	$13.036$	$\Q(i, \sqrt{19})$	None		$2$	$0$	$0$	$0$	$1064$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(266+3\beta _{2})q^{5}+(-7\beta _{1}+\cdots)q^{7}+\cdots$
32.9.d.a	$32$	$9$	32.d	8.d	$2$	$1$	$1$	$13.036$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$-34$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-34q^{3}-5405q^{9}+27166q^{11}+\cdots$
32.9.d.b	$32$	$9$	32.d	8.d	$2$	$6$	$6$	$13.036$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$0$	$36$	$0$	$0$		$2^{33}$	$\mathrm{SU}(2)[C_{2}]$	$q+(6+\beta _{1})q^{3}-\beta _{2}q^{5}+(-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
32.9.h.a	$32$	$9$	32.h	32.h	$8$	$124$	$31$	$13.036$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
32.10.a.a	$32$	$10$	32.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$2398$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+2398q^{5}-3^{9}q^{9}+112806q^{13}+\cdots$
32.10.a.b	$32$	$10$	32.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{106}) $	None	✓	$1$	$1$	$0$	$-176$	$1404$	$-2784$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-88+\beta )q^{3}+(702-8\beta )q^{5}+(-1392+\cdots)q^{7}+\cdots$
32.10.a.c	$32$	$10$	32.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$0$	$-4420$	$0$	$-$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2210q^{5}-42\beta q^{7}+26397q^{9}+\cdots$
32.10.a.d	$32$	$10$	32.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{7}) $	None	✓	$2$	$1$	$0$	$0$	$-68$	$0$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta q^{3}-34q^{5}-86\beta q^{7}-3555q^{9}+\cdots$
32.10.a.e	$32$	$10$	32.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{106}) $	None	✓	$1$	$0$	$0$	$176$	$1404$	$2784$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(88+\beta )q^{3}+(702+8\beta )q^{5}+(1392+\cdots)q^{7}+\cdots$
32.10.b.a	$32$	$10$	32.b	8.b	$2$	$8$	$8$	$16.481$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-4800$		$2^{56}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-600-\beta _{3}+\cdots)q^{7}+\cdots$
32.10.g.a	$32$	$10$	32.g	32.g	$8$	$140$	$35$	$16.481$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
32.11.c.a	$32$	$11$	32.c	4.b	$2$	$4$	$4$	$20.331$	$\Q(i, \sqrt{30})$	None		$2$	$0$	$0$	$0$	$-1400$	$0$		$2^{17}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{3}+(-350-\beta _{3})q^{5}+\cdots$
32.11.c.b	$32$	$11$	32.c	4.b	$2$	$6$	$6$	$20.331$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$0$	$0$	$-1716$	$0$		$2^{47}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-286+\beta _{2})q^{5}+(58\beta _{1}+\cdots)q^{7}+\cdots$
32.11.d.a	$32$	$11$	32.d	8.d	$2$	$1$	$1$	$20.331$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$482$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+482q^{3}+173275q^{9}+97426q^{11}+\cdots$
32.11.d.b	$32$	$11$	32.d	8.d	$2$	$8$	$8$	$20.331$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$-480$	$0$	$0$		$2^{57}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-60+\beta _{1})q^{3}+\beta _{3}q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
32.11.h.a	$32$	$11$	32.h	32.h	$8$	$156$	$39$	$20.331$		None		$2$	$0$	$-4$	$-4$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.