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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 129 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
121.2.a.a	$121$	$2$	121.a	1.a	$1$	$1$	$1$	$0.966$	$\Q$	None	✓	✓			121.2.a.a	$1$	$0$	$-1$	$2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots$
121.2.a.b	$121$	$2$	121.a	1.a	$1$	$1$	$1$	$0.966$	$\Q$	$\Q(\sqrt{-11}) $	✓	✓	✓	✓	121.2.a.b	$2$	$1$	$0$	$-1$	$-3$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-q^{3}-2q^{4}-3q^{5}-2q^{9}+2q^{12}+\cdots$
121.2.a.c	$121$	$2$	121.a	1.a	$1$	$1$	$1$	$0.966$	$\Q$	None	✓	✓			121.2.a.a	$1$	$0$	$1$	$2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}-q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots$
121.2.a.d	$121$	$2$	121.a	1.a	$1$	$1$	$1$	$0.966$	$\Q$	None	✓				11.2.a.a	$1$	$0$	$2$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots$
121.2.c.a	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	None					11.2.a.a	$4$	$0$	$-2$	$1$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
121.2.c.b	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	None		✓			121.2.a.a	$4$	$0$	$-1$	$-2$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
121.2.c.c	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	$\Q(\sqrt{-11}) $		✓			121.2.a.b	$8$	$0$	$0$	$1$	$3$	$0$		$1$	$\mathrm{U}(1)[D_{5}]$	$q-\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}+3\zeta_{10}q^{5}+\cdots$
121.2.c.d	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	None		✓			121.2.a.a	$4$	$0$	$1$	$-2$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+2\zeta_{10}^{2}q^{3}+\cdots$
121.2.c.e	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	None					11.2.a.a	$4$	$0$	$2$	$1$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots$
121.2.e.a	$121$	$2$	121.e	121.e	$11$	$100$	$10$	$0.966$		None		✓	✓	✓	121.2.e.a	$2$	$0$	$-6$	$-18$	$-7$	$-1$			$\mathrm{SU}(2)[C_{11}]$
121.2.g.a	$121$	$2$	121.g	121.g	$55$	$400$	$10$	$0.966$		None		✓	✓	✓	121.2.g.a	$2$	$0$	$-44$	$-32$	$-43$	$-44$			$\mathrm{SU}(2)[C_{55}]$
121.3.b.a	$121$	$3$	121.b	11.b	$2$	$2$	$2$	$3.297$	$\Q(\sqrt{-2}) $	None		✓			121.3.b.a	$2$	$0$	$0$	$-2$	$-14$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-q^{3}+2q^{4}-7q^{5}-\beta q^{6}+\cdots$
121.3.b.b	$121$	$3$	121.b	11.b	$2$	$4$	$4$	$3.297$	$\Q(\zeta_{10})$	None					11.3.d.a	$2$	$0$	$0$	$10$	$16$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{10}-\zeta_{10}^{3})q^{2}+(2-\zeta_{10}^{2})q^{3}+\cdots$
121.3.b.c	$121$	$3$	121.b	11.b	$2$	$8$	$8$	$3.297$	8.0.$\cdots$.1	None		✓	✓		121.3.b.c	$2$	$0$	$0$	$-4$	$-4$	$0$		$2\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{3}+\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots$
121.3.d.a	$121$	$3$	121.d	11.d	$10$	$4$	$1$	$3.297$	$\Q(\zeta_{10})$	None					11.3.d.a	$2$	$0$	$-5$	$-5$	$-4$	$20$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-2-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(-3+\cdots)q^{3}+\cdots$
121.3.d.b	$121$	$3$	121.d	11.d	$10$	$4$	$1$	$3.297$	$\Q(\zeta_{10})$	$\Q(\sqrt{-11}) $					11.3.b.a	$8$	$0$	$0$	$5$	$1$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(5-5\zeta_{10}+5\zeta_{10}^{2}-5\zeta_{10}^{3})q^{3}+\cdots$
121.3.d.c	$121$	$3$	121.d	11.d	$10$	$4$	$1$	$3.297$	$\Q(\zeta_{10})$	None					11.3.d.a	$2$	$0$	$5$	$-5$	$-4$	$-20$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-3+2\zeta_{10}+\cdots)q^{3}+\cdots$
121.3.d.d	$121$	$3$	121.d	11.d	$10$	$4$	$1$	$3.297$	$\Q(\zeta_{10})$	None					11.3.d.a	$2$	$0$	$5$	$0$	$-4$	$-10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots$
121.3.d.e	$121$	$3$	121.d	11.d	$10$	$8$	$2$	$3.297$	8.0.64000000.1	None		✓			121.3.b.a	$8$	$0$	$0$	$2$	$14$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}-2\beta _{2}q^{4}+\cdots$
121.3.d.f	$121$	$3$	121.d	11.d	$10$	$32$	$8$	$3.297$		None		✓	✓		121.3.b.c	$8$	$0$	$0$	$4$	$4$	$0$			$\mathrm{SU}(2)[C_{10}]$
121.3.f.a	$121$	$3$	121.f	121.f	$22$	$210$	$21$	$3.297$		None		✓	✓	✓	121.3.f.a	$2$	$0$	$-11$	$-16$	$-7$	$-11$			$\mathrm{SU}(2)[C_{22}]$
121.3.h.a	$121$	$3$	121.h	121.h	$110$	$840$	$21$	$3.297$		None		✓	✓	✓	121.3.h.a	$2$	$0$	$-39$	$-34$	$-43$	$-54$			$\mathrm{SU}(2)[C_{110}]$
121.4.a.a	$121$	$4$	121.a	1.a	$1$	$1$	$1$	$7.139$	$\Q$	$\Q(\sqrt{-11}) $	✓	✓			121.4.a.a	$2$	$0$	$0$	$8$	$18$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+8q^{3}-8q^{4}+18q^{5}+37q^{9}-2^{6}q^{12}+\cdots$
121.4.a.b	$121$	$4$	121.a	1.a	$1$	$2$	$2$	$7.139$	$\Q(\sqrt{3}) $	None	✓	✓			121.4.a.b	$1$	$1$	$-2$	$-8$	$-10$	$-8$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-4+\beta )q^{3}+(5-2\beta )q^{4}+\cdots$
121.4.a.c	$121$	$4$	121.a	1.a	$1$	$2$	$2$	$7.139$	$\Q(\sqrt{3}) $	None	✓				11.4.a.a	$1$	$1$	$-2$	$-2$	$2$	$-20$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots$
121.4.a.d	$121$	$4$	121.a	1.a	$1$	$2$	$2$	$7.139$	$\Q(\sqrt{26}) $	None	✓	✓			121.4.a.d	$2$	$0$	$0$	$-10$	$10$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-5q^{3}+18q^{4}+5q^{5}-5\beta q^{6}+\cdots$
121.4.a.e	$121$	$4$	121.a	1.a	$1$	$2$	$2$	$7.139$	$\Q(\sqrt{3}) $	None	✓	✓			121.4.a.b	$1$	$1$	$2$	$-8$	$-10$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-4-\beta )q^{3}+(5+2\beta )q^{4}+\cdots$
121.4.a.f	$121$	$4$	121.a	1.a	$1$	$4$	$4$	$7.139$	$\Q(\sqrt{5}, \sqrt{37})$	None	✓		✓		11.4.c.a	$1$	$1$	$-4$	$6$	$-11$	$-25$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2})q^{3}+\cdots$
121.4.a.g	$121$	$4$	121.a	1.a	$1$	$4$	$4$	$7.139$	$\Q(\sqrt{5}, \sqrt{37})$	None	✓				11.4.c.a	$1$	$0$	$4$	$6$	$-11$	$25$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(2+\beta _{2})q^{3}+(3+\cdots)q^{4}+\cdots$
121.4.a.h	$121$	$4$	121.a	1.a	$1$	$6$	$6$	$7.139$	6.6.$\cdots$.1	None	✓	✓	✓		121.4.a.h	$2$	$0$	$0$	$8$	$14$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(3+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
121.4.c.a	$121$	$4$	121.c	11.c	$5$	$4$	$1$	$7.139$	$\Q(\zeta_{10})$	$\Q(\sqrt{-11}) $		✓			121.4.a.a	$8$	$0$	$0$	$-8$	$-18$	$0$		$1$	$\mathrm{U}(1)[D_{5}]$	$q+8\zeta_{10}^{2}q^{3}+8\zeta_{10}^{3}q^{4}-18\zeta_{10}q^{5}+\cdots$
121.4.c.b	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.$\cdots$.1	None					11.4.c.a	$2$	$0$	$-3$	$-3$	$18$	$-10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
121.4.c.c	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None					11.4.a.a	$4$	$0$	$-2$	$2$	$-2$	$-20$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+\beta _{7})q^{2}+(-4\beta _{1}-\beta _{6})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
121.4.c.d	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None		✓			121.4.a.b	$4$	$0$	$-2$	$8$	$10$	$-8$		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}-\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots$
121.4.c.e	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.$\cdots$.7	None		✓			121.4.a.d	$8$	$0$	$0$	$10$	$-10$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}-5\beta _{6}q^{3}+18\beta _{4}q^{4}+(-5+\cdots)q^{5}+\cdots$
121.4.c.f	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None					11.4.a.a	$4$	$0$	$2$	$2$	$-2$	$20$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}+\beta _{7})q^{2}+(4\beta _{1}-\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots$
121.4.c.g	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None		✓			121.4.a.b	$4$	$0$	$2$	$8$	$10$	$8$		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}+\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots$
121.4.c.h	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.$\cdots$.1	None					11.4.c.a	$2$	$0$	$3$	$-3$	$18$	$10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+2\beta _{4}+\beta _{6}-\beta _{7})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
121.4.c.i	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.$\cdots$.1	None					11.4.c.a	$2$	$0$	$7$	$-3$	$-7$	$35$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots$
121.4.c.j	$121$	$4$	121.c	11.c	$5$	$24$	$6$	$7.139$		None		✓	✓		121.4.a.h	$8$	$0$	$0$	$-8$	$-14$	$0$			$\mathrm{SU}(2)[C_{5}]$
121.4.e.a	$121$	$4$	121.e	121.e	$11$	$320$	$32$	$7.139$		None		✓	✓	✓	121.4.e.a	$2$	$0$	$-13$	$-18$	$-17$	$-31$			$\mathrm{SU}(2)[C_{11}]$
121.4.g.a	$121$	$4$	121.g	121.g	$55$	$1280$	$32$	$7.139$		None		✓	✓	✓	121.4.g.a	$2$	$0$	$-37$	$-32$	$-33$	$-9$			$\mathrm{SU}(2)[C_{55}]$
121.5.b.a	$121$	$5$	121.b	11.b	$2$	$8$	$8$	$12.508$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			121.5.b.a	$2$	$0$	$0$	$10$	$-42$	$0$		$2^{4}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(-12+\beta _{2}+\cdots)q^{4}+\cdots$
121.5.b.b	$121$	$5$	121.b	11.b	$2$	$12$	$12$	$12.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					11.5.d.a	$2$	$0$	$0$	$-26$	$-28$	$0$		$2^{6}\cdot 11^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-2+\beta _{3})q^{3}+(-6+\beta _{7}+\cdots)q^{4}+\cdots$
121.5.b.c	$121$	$5$	121.b	11.b	$2$	$12$	$12$	$12.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			121.5.b.c	$2$	$0$	$0$	$20$	$60$	$0$		$2\cdot 11^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(2-\beta _{4})q^{3}+(-6+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
121.5.d.a	$121$	$5$	121.d	11.d	$10$	$4$	$1$	$12.508$	$\Q(\zeta_{10})$	$\Q(\sqrt{-11}) $					11.5.b.a	$8$	$0$	$0$	$-7$	$49$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(-7+7\zeta_{10}-7\zeta_{10}^{2}+7\zeta_{10}^{3})q^{3}+\cdots$
121.5.d.b	$121$	$5$	121.d	11.d	$10$	$8$	$2$	$12.508$	8.0.5184000000.5	None					11.5.b.b	$8$	$0$	$0$	$6$	$-62$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{4}+\beta _{5}+\beta _{6}+\beta _{7})q^{2}+3\beta _{1}q^{3}+\cdots$
121.5.d.c	$121$	$5$	121.d	11.d	$10$	$12$	$3$	$12.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					11.5.d.a	$2$	$0$	$-15$	$19$	$32$	$200$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\beta _{1}+\beta _{3}-\beta _{6}-\beta _{7}+\beta _{8}+\cdots)q^{2}+\cdots$
121.5.d.d	$121$	$5$	121.d	11.d	$10$	$12$	$3$	$12.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					11.5.d.a	$2$	$0$	$5$	$-6$	$-18$	$80$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1+\beta _{2}+2\beta _{3}+\beta _{4}-\beta _{7})q^{2}+(1+\cdots)q^{3}+\cdots$
121.5.d.e	$121$	$5$	121.d	11.d	$10$	$12$	$3$	$12.508$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					11.5.d.a	$2$	$0$	$15$	$19$	$32$	$-200$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7}-\beta _{8})q^{2}+\cdots$

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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.