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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 302 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
64.2.a.a	$64$	$2$	64.a	1.a	$1$	$1$	$1$	$0.511$	$\Q$	$\Q(\sqrt{-1}) $	✓		✓	✓	32.2.a.a	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+2q^{5}-3q^{9}-6q^{13}+2q^{17}-q^{25}+\cdots$
64.2.b.a	$64$	$2$	64.b	8.b	$2$	$2$	$2$	$0.511$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-2}) $		✓	✓	✓	64.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}-q^{9}-3\beta q^{11}-6 q^{17}+\beta q^{19}+\cdots$
64.2.e.a	$64$	$2$	64.e	16.e	$4$	$2$	$1$	$0.511$	$\Q(\sqrt{-1}) $	None			✓	✓	16.2.e.a	$2$	$0$	$0$	$2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{3}+(-i-1)q^{5}+2 i q^{7}+\cdots$
64.2.i.a	$64$	$2$	64.i	64.i	$16$	$56$	$7$	$0.511$		None		✓	✓	✓	64.2.i.a	$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
64.3.c.a	$64$	$3$	64.c	4.b	$2$	$1$	$1$	$1.744$	$\Q$	$\Q(\sqrt{-1}) $	✓				16.3.c.a	$2$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+6q^{5}+9q^{9}-10q^{13}-30q^{17}+\cdots$
64.3.c.b	$64$	$3$	64.c	4.b	$2$	$2$	$2$	$1.744$	$\Q(\sqrt{-1}) $	None			✓		32.3.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-2 q^{5}+2\beta q^{7}-7 q^{9}-\beta q^{11}+\cdots$
64.3.d.a	$64$	$3$	64.d	8.d	$2$	$4$	$4$	$1.744$	$\Q(\zeta_{12})$	None		✓	✓	✓	64.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}-\beta_{2} q^{5}-\beta_{3} q^{7}+3 q^{9}+\cdots$
64.3.f.a	$64$	$3$	64.f	16.f	$4$	$6$	$3$	$1.744$	6.0.399424.1	None			✓	✓	16.3.f.a	$2$	$0$	$0$	$2$	$-2$	$4$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{5})q^{5}+\cdots$
64.3.j.a	$64$	$3$	64.j	64.j	$16$	$120$	$15$	$1.744$		None		✓	✓	✓	64.3.j.a	$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
64.4.a.a	$64$	$4$	64.a	1.a	$1$	$1$	$1$	$3.776$	$\Q$	None	✓				32.4.a.a	$1$	$0$	$0$	$-8$	$10$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}+10q^{5}+2^{4}q^{7}+37q^{9}+40q^{11}+\cdots$
64.4.a.b	$64$	$4$	64.a	1.a	$1$	$1$	$1$	$3.776$	$\Q$	None	✓				8.4.a.a	$1$	$1$	$0$	$-4$	$2$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}+2q^{5}-24q^{7}-11q^{9}-44q^{11}+\cdots$
64.4.a.c	$64$	$4$	64.a	1.a	$1$	$1$	$1$	$3.776$	$\Q$	$\Q(\sqrt{-1}) $	✓				32.4.a.b	$2$	$1$	$0$	$0$	$-22$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-22q^{5}-3^{3}q^{9}+18q^{13}-94q^{17}+\cdots$
64.4.a.d	$64$	$4$	64.a	1.a	$1$	$1$	$1$	$3.776$	$\Q$	None	✓				8.4.a.a	$1$	$0$	$0$	$4$	$2$	$24$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{3}+2q^{5}+24q^{7}-11q^{9}+44q^{11}+\cdots$
64.4.a.e	$64$	$4$	64.a	1.a	$1$	$1$	$1$	$3.776$	$\Q$	None	✓				32.4.a.a	$1$	$0$	$0$	$8$	$10$	$-16$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{3}+10q^{5}-2^{4}q^{7}+37q^{9}-40q^{11}+\cdots$
64.4.b.a	$64$	$4$	64.b	8.b	$2$	$2$	$2$	$3.776$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-2}) $		✓			64.4.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+5\beta q^{3}-73 q^{9}+9\beta q^{11}+90 q^{17}+\cdots$
64.4.b.b	$64$	$4$	64.b	8.b	$2$	$4$	$4$	$3.776$	$\Q(\zeta_{12})$	None		✓	✓		64.4.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}-\beta_{2} q^{5}+\beta_{3} q^{7}+23 q^{9}+\cdots$
64.4.e.a	$64$	$4$	64.e	16.e	$4$	$10$	$5$	$3.776$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None			✓	✓	16.4.e.a	$2$	$0$	$0$	$2$	$-2$	$0$		$2^{20}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{5}q^{3}+\beta _{3}q^{5}+(3\beta _{1}-\beta _{4})q^{7}+(5\beta _{1}+\cdots)q^{9}+\cdots$
64.4.i.a	$64$	$4$	64.i	64.i	$16$	$184$	$23$	$3.776$		None		✓	✓	✓	64.4.i.a	$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
64.5.c.a	$64$	$5$	64.c	4.b	$2$	$1$	$1$	$6.616$	$\Q$	$\Q(\sqrt{-1}) $	✓				4.5.b.a	$2$	$0$	$0$	$0$	$14$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+14q^{5}+3^{4}q^{9}+238q^{13}+322q^{17}+\cdots$
64.5.c.b	$64$	$5$	64.c	4.b	$2$	$2$	$2$	$6.616$	$\Q(\sqrt{-1}) $	None					32.5.c.b	$2$	$0$	$0$	$0$	$-52$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-26 q^{5}-22\beta q^{7}+65 q^{9}+\cdots$
64.5.c.c	$64$	$5$	64.c	4.b	$2$	$2$	$2$	$6.616$	$\Q(\sqrt{-3}) $	None					16.5.c.a	$2$	$0$	$0$	$0$	$-36$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-18 q^{5}-2\beta q^{7}-111 q^{9}+\cdots$
64.5.c.d	$64$	$5$	64.c	4.b	$2$	$2$	$2$	$6.616$	$\Q(\sqrt{-1}) $	None					32.5.c.a	$2$	$0$	$0$	$0$	$76$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+3\beta q^{3}+38 q^{5}-2\beta q^{7}-63 q^{9}+\cdots$
64.5.d.a	$64$	$5$	64.d	8.d	$2$	$4$	$4$	$6.616$	$\Q(\zeta_{12})$	None		✓			64.5.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}-3\beta_{2} q^{5}+5\beta_{3} q^{7}-69 q^{9}+\cdots$
64.5.d.b	$64$	$5$	64.d	8.d	$2$	$4$	$4$	$6.616$	$\Q(i, \sqrt{51})$	None		✓			64.5.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+7\beta _{2}q^{7}+123q^{9}+\cdots$
64.5.f.a	$64$	$5$	64.f	16.f	$4$	$14$	$7$	$6.616$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None			✓	✓	16.5.f.a	$2$	$0$	$0$	$2$	$-2$	$4$		$2^{42}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+\beta _{3}q^{5}+\beta _{9}q^{7}+(19\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
64.5.j.a	$64$	$5$	64.j	64.j	$16$	$248$	$31$	$6.616$		None		✓	✓	✓	64.5.j.a	$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
64.6.a.a	$64$	$6$	64.a	1.a	$1$	$1$	$1$	$10.265$	$\Q$	None	✓				8.6.a.a	$1$	$1$	$0$	$-20$	$74$	$-24$	$+$	$1$	$\mathrm{SU}(2)$	$q-20q^{3}+74q^{5}-24q^{7}+157q^{9}+\cdots$
64.6.a.b	$64$	$6$	64.a	1.a	$1$	$1$	$1$	$10.265$	$\Q$	None	✓				4.6.a.a	$1$	$0$	$0$	$-12$	$-54$	$88$	$-$	$1$	$\mathrm{SU}(2)$	$q-12q^{3}-54q^{5}+88q^{7}-99q^{9}+\cdots$
64.6.a.c	$64$	$6$	64.a	1.a	$1$	$1$	$1$	$10.265$	$\Q$	None	✓				32.6.a.a	$1$	$1$	$0$	$-8$	$-14$	$208$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}-14q^{5}+208q^{7}-179q^{9}+\cdots$
64.6.a.d	$64$	$6$	64.a	1.a	$1$	$1$	$1$	$10.265$	$\Q$	$\Q(\sqrt{-1}) $	✓				32.6.a.b	$2$	$0$	$0$	$0$	$82$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+82q^{5}-3^{5}q^{9}+1194q^{13}+2242q^{17}+\cdots$
64.6.a.e	$64$	$6$	64.a	1.a	$1$	$1$	$1$	$10.265$	$\Q$	None	✓				32.6.a.a	$1$	$1$	$0$	$8$	$-14$	$-208$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{3}-14q^{5}-208q^{7}-179q^{9}+\cdots$
64.6.a.f	$64$	$6$	64.a	1.a	$1$	$1$	$1$	$10.265$	$\Q$	None	✓				4.6.a.a	$1$	$1$	$0$	$12$	$-54$	$-88$	$+$	$1$	$\mathrm{SU}(2)$	$q+12q^{3}-54q^{5}-88q^{7}-99q^{9}+\cdots$
64.6.a.g	$64$	$6$	64.a	1.a	$1$	$1$	$1$	$10.265$	$\Q$	None	✓				8.6.a.a	$1$	$0$	$0$	$20$	$74$	$24$	$-$	$1$	$\mathrm{SU}(2)$	$q+20q^{3}+74q^{5}+24q^{7}+157q^{9}+\cdots$
64.6.a.h	$64$	$6$	64.a	1.a	$1$	$2$	$2$	$10.265$	$\Q(\sqrt{3}) $	None	✓		✓		32.6.a.d	$2$	$0$	$0$	$0$	$-92$	$0$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta q^{3}-46q^{5}+6\beta q^{7}+525q^{9}+\cdots$
64.6.b.a	$64$	$6$	64.b	8.b	$2$	$2$	$2$	$10.265$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-2}) $		✓			64.6.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}+239 q^{9}+237\beta q^{11}+1914 q^{17}+\cdots$
64.6.b.b	$64$	$6$	64.b	8.b	$2$	$8$	$8$	$10.265$	8.0.$\cdots$.15	None		✓	✓		64.6.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{42}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+(-161+\cdots)q^{9}+\cdots$
64.6.e.a	$64$	$6$	64.e	16.e	$4$	$18$	$9$	$10.265$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None			✓	✓	16.6.e.a	$2$	$0$	$0$	$2$	$-2$	$0$		$2^{72}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{3}-\beta _{5}q^{5}+(-11\beta _{1}+\beta _{4})q^{7}+\cdots$
64.6.i.a	$64$	$6$	64.i	64.i	$16$	$312$	$39$	$10.265$		None		✓	✓	✓	64.6.i.a	$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
64.7.c.a	$64$	$7$	64.c	4.b	$2$	$1$	$1$	$14.723$	$\Q$	$\Q(\sqrt{-1}) $	✓				16.7.c.a	$2$	$0$	$0$	$0$	$-234$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-234q^{5}+3^{6}q^{9}+4070q^{13}-990q^{17}+\cdots$
64.7.c.b	$64$	$7$	64.c	4.b	$2$	$2$	$2$	$14.723$	$\Q(\sqrt{-1}) $	None					32.7.c.a	$2$	$0$	$0$	$0$	$-100$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-50 q^{5}-46\beta q^{7}+713 q^{9}+\cdots$
64.7.c.c	$64$	$7$	64.c	4.b	$2$	$2$	$2$	$14.723$	$\Q(\sqrt{-15}) $	None					4.7.b.a	$2$	$0$	$0$	$0$	$-20$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-10q^{5}-10\beta q^{7}-231q^{9}+\cdots$
64.7.c.d	$64$	$7$	64.c	4.b	$2$	$2$	$2$	$14.723$	$\Q(\sqrt{-3}) $	None					16.7.c.b	$2$	$0$	$0$	$0$	$300$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+150 q^{5}+22\beta q^{7}-39 q^{9}+\cdots$
64.7.c.e	$64$	$7$	64.c	4.b	$2$	$4$	$4$	$14.723$	$\Q(i, \sqrt{6})$	None			✓		32.7.c.b	$2$	$0$	$0$	$0$	$56$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(14+\beta _{3})q^{5}+(-2\beta _{1}+5\beta _{2}+\cdots)q^{7}+\cdots$
64.7.d.a	$64$	$7$	64.d	8.d	$2$	$4$	$4$	$14.723$	$\Q(i, \sqrt{11})$	None		✓			64.7.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-5\beta _{3}q^{5}-11\beta _{2}q^{7}-333q^{9}+\cdots$
64.7.d.b	$64$	$7$	64.d	8.d	$2$	$8$	$8$	$14.723$	8.0.$\cdots$.9	None		✓	✓		64.7.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{40}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-\beta _{3}q^{5}+(-\beta _{6}+\beta _{7})q^{7}+\cdots$
64.7.f.a	$64$	$7$	64.f	16.f	$4$	$22$	$11$	$14.723$		None			✓	✓	16.7.f.a	$2$	$0$	$0$	$2$	$-2$	$4$			$\mathrm{SU}(2)[C_{4}]$
64.7.j.a	$64$	$7$	64.j	64.j	$16$	$376$	$47$	$14.723$		None		✓	✓	✓	64.7.j.a	$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
64.8.a.a	$64$	$8$	64.a	1.a	$1$	$1$	$1$	$19.993$	$\Q$	None	✓				8.8.a.a	$1$	$1$	$0$	$-84$	$82$	$456$	$-$	$1$	$\mathrm{SU}(2)$	$q-84q^{3}+82q^{5}+456q^{7}+4869q^{9}+\cdots$
64.8.a.b	$64$	$8$	64.a	1.a	$1$	$1$	$1$	$19.993$	$\Q$	None	✓				8.8.a.b	$1$	$0$	$0$	$-44$	$-430$	$-1224$	$+$	$1$	$\mathrm{SU}(2)$	$q-44q^{3}-430q^{5}-1224q^{7}-251q^{9}+\cdots$
64.8.a.c	$64$	$8$	64.a	1.a	$1$	$1$	$1$	$19.993$	$\Q$	None	✓				2.8.a.a	$1$	$0$	$0$	$-12$	$210$	$1016$	$+$	$1$	$\mathrm{SU}(2)$	$q-12q^{3}+210q^{5}+1016q^{7}-2043q^{9}+\cdots$

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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.