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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 254 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
42.2.a.a	$42$	$2$	42.a	1.a	$1$	$1$	$1$	$0.335$	$\Q$	None	✓	✓	✓	✓	42.2.a.a	$1$	$0$	$1$	$-1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
42.2.d.a	$42$	$2$	42.d	21.c	$2$	$4$	$4$	$0.335$	$\Q(i, \sqrt{6})$	None		✓	✓	✓	42.2.d.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
42.2.e.a	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	$\Q(\sqrt{-3}) $	None		✓			42.2.e.a	$2$	$0$	$-1$	$1$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots$
42.2.e.b	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	$\Q(\sqrt{-3}) $	None		✓			42.2.e.b	$2$	$0$	$1$	$-1$	$-3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots$
42.2.f.a	$42$	$2$	42.f	21.g	$6$	$4$	$2$	$0.335$	$\Q(\zeta_{12})$	None		✓	✓	✓	42.2.f.a	$4$	$0$	$0$	$0$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
42.3.b.a	$42$	$3$	42.b	3.b	$2$	$4$	$4$	$1.144$	$\Q(\sqrt{-2}, \sqrt{7})$	None		✓	✓	✓	42.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}-2q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
42.3.c.a	$42$	$3$	42.c	7.b	$2$	$4$	$4$	$1.144$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓	✓	✓	42.3.c.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+(-2\beta _{2}-\beta _{3})q^{5}+\cdots$
42.3.g.a	$42$	$3$	42.g	7.d	$6$	$4$	$2$	$1.144$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓	✓	✓	42.3.g.a	$2$	$0$	$0$	$6$	$12$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots$
42.3.h.a	$42$	$3$	42.h	21.h	$6$	$4$	$2$	$1.144$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			42.3.h.a	$4$	$0$	$0$	$2$	$0$	$-14$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{2}-2\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$
42.3.h.b	$42$	$3$	42.h	21.h	$6$	$8$	$4$	$1.144$	8.0.4857532416.2	None		✓	✓		42.3.h.b	$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}-\beta _{6})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
42.4.a.a	$42$	$4$	42.a	1.a	$1$	$1$	$1$	$2.478$	$\Q$	None	✓	✓	✓	✓	42.4.a.a	$1$	$0$	$2$	$-3$	$18$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+18q^{5}-6q^{6}+\cdots$
42.4.a.b	$42$	$4$	42.a	1.a	$1$	$1$	$1$	$2.478$	$\Q$	None	✓	✓	✓	✓	42.4.a.b	$1$	$0$	$2$	$3$	$2$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+2q^{5}+6q^{6}+\cdots$
42.4.d.a	$42$	$4$	42.d	21.c	$2$	$8$	$8$	$2.478$	8.0.$\cdots$.13	None		✓	✓	✓	42.4.d.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{5}q^{3}-4q^{4}+(2\beta _{5}-2\beta _{6}+\cdots)q^{5}+\cdots$
42.4.e.a	$42$	$4$	42.e	7.c	$3$	$2$	$1$	$2.478$	$\Q(\sqrt{-3}) $	None		✓			42.4.e.a	$2$	$0$	$2$	$-3$	$6$	$-7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots$
42.4.e.b	$42$	$4$	42.e	7.c	$3$	$2$	$1$	$2.478$	$\Q(\sqrt{-3}) $	None		✓			42.4.e.b	$2$	$0$	$2$	$3$	$15$	$35$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots$
42.4.e.c	$42$	$4$	42.e	7.c	$3$	$4$	$2$	$2.478$	$\Q(\sqrt{-3}, \sqrt{1345})$	None		✓	✓		42.4.e.c	$2$	$0$	$-4$	$-6$	$-5$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\beta _{2}q^{2}+(-3+3\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots$
42.4.f.a	$42$	$4$	42.f	21.g	$6$	$16$	$8$	$2.478$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	42.4.f.a	$4$	$0$	$0$	$0$	$0$	$80$		$2^{6}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(4+4\beta _{5})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
42.5.b.a	$42$	$5$	42.b	3.b	$2$	$8$	$8$	$4.342$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓	✓	42.5.b.a	$2$	$0$	$0$	$12$	$0$	$0$		$2^{7}\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(2-\beta _{3})q^{3}-8q^{4}+(-4\beta _{1}+\cdots)q^{5}+\cdots$
42.5.c.a	$42$	$5$	42.c	7.b	$2$	$4$	$4$	$4.342$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓	✓	✓	42.5.c.a	$2$	$0$	$0$	$0$	$0$	$20$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-3\beta _{2}q^{3}+8q^{4}+(-4\beta _{2}+\cdots)q^{5}+\cdots$
42.5.g.a	$42$	$5$	42.g	7.d	$6$	$4$	$2$	$4.342$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			42.5.g.a	$2$	$0$	$0$	$-18$	$-66$	$-70$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-6-3\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots$
42.5.g.b	$42$	$5$	42.g	7.d	$6$	$8$	$4$	$4.342$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓		42.5.g.b	$2$	$0$	$0$	$36$	$-42$	$76$		$2^{4}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(6+3\beta _{1})q^{3}+8\beta _{1}q^{4}+(-3+\cdots)q^{5}+\cdots$
42.5.h.a	$42$	$5$	42.h	21.h	$6$	$20$	$10$	$4.342$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	42.5.h.a	$4$	$0$	$0$	$0$	$0$	$130$		$2^{12}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{9})q^{2}-\beta _{10}q^{3}+(8+8\beta _{2}+\cdots)q^{4}+\cdots$
42.6.a.a	$42$	$6$	42.a	1.a	$1$	$1$	$1$	$6.736$	$\Q$	None	✓	✓	✓	✓	42.6.a.a	$1$	$0$	$-4$	$-9$	$-54$	$49$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-9q^{3}+2^{4}q^{4}-54q^{5}+6^{2}q^{6}+\cdots$
42.6.a.b	$42$	$6$	42.a	1.a	$1$	$1$	$1$	$6.736$	$\Q$	None	✓	✓	✓	✓	42.6.a.b	$1$	$1$	$-4$	$-9$	$44$	$-49$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-9q^{3}+2^{4}q^{4}+44q^{5}+6^{2}q^{6}+\cdots$
42.6.a.c	$42$	$6$	42.a	1.a	$1$	$1$	$1$	$6.736$	$\Q$	None	✓	✓	✓	✓	42.6.a.c	$1$	$1$	$-4$	$9$	$-72$	$49$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+9q^{3}+2^{4}q^{4}-72q^{5}-6^{2}q^{6}+\cdots$
42.6.a.d	$42$	$6$	42.a	1.a	$1$	$1$	$1$	$6.736$	$\Q$	None	✓	✓	✓	✓	42.6.a.d	$1$	$0$	$-4$	$9$	$26$	$-49$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+9q^{3}+2^{4}q^{4}+26q^{5}-6^{2}q^{6}+\cdots$
42.6.a.e	$42$	$6$	42.a	1.a	$1$	$1$	$1$	$6.736$	$\Q$	None	✓	✓	✓	✓	42.6.a.e	$1$	$0$	$4$	$-9$	$76$	$-49$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-9q^{3}+2^{4}q^{4}+76q^{5}-6^{2}q^{6}+\cdots$
42.6.a.f	$42$	$6$	42.a	1.a	$1$	$1$	$1$	$6.736$	$\Q$	None	✓	✓	✓	✓	42.6.a.f	$1$	$0$	$4$	$9$	$24$	$49$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+9q^{3}+2^{4}q^{4}+24q^{5}+6^{2}q^{6}+\cdots$
42.6.d.a	$42$	$6$	42.d	21.c	$2$	$12$	$12$	$6.736$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	42.6.d.a	$4$	$0$	$0$	$0$	$0$	$-252$		$2^{15}\cdot 3^{6}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}-2^{4}q^{4}+(\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
42.6.e.a	$42$	$6$	42.e	7.c	$3$	$2$	$1$	$6.736$	$\Q(\sqrt{-3}) $	None		✓			42.6.e.a	$2$	$0$	$-4$	$-9$	$6$	$119$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-4+4\zeta_{6})q^{2}-9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+\cdots$
42.6.e.b	$42$	$6$	42.e	7.c	$3$	$2$	$1$	$6.736$	$\Q(\sqrt{-3}) $	None		✓			42.6.e.b	$2$	$0$	$4$	$9$	$-86$	$49$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(4-4\zeta_{6})q^{2}+9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+\cdots$
42.6.e.c	$42$	$6$	42.e	7.c	$3$	$4$	$2$	$6.736$	$\Q(\sqrt{-3}, \sqrt{9601})$	None		✓			42.6.e.c	$2$	$0$	$-8$	$18$	$53$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-4\beta _{2}q^{2}+(9-9\beta _{2})q^{3}+(-2^{4}+2^{4}\beta _{2}+\cdots)q^{4}+\cdots$
42.6.e.d	$42$	$6$	42.e	7.c	$3$	$4$	$2$	$6.736$	$\Q(\sqrt{-3}, \sqrt{505})$	None		✓			42.6.e.d	$2$	$0$	$8$	$-18$	$-17$	$-408$		$7$	$\mathrm{SU}(2)[C_{3}]$	$q+(4-4\beta _{1})q^{2}-9\beta _{1}q^{3}-2^{4}\beta _{1}q^{4}+\cdots$
42.6.f.a	$42$	$6$	42.f	21.g	$6$	$28$	$14$	$6.736$		None		✓	✓	✓	42.6.f.a	$4$	$0$	$0$	$0$	$0$	$-154$			$\mathrm{SU}(2)[C_{6}]$
42.7.b.a	$42$	$7$	42.b	3.b	$2$	$12$	$12$	$9.662$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	42.7.b.a	$2$	$0$	$0$	$-84$	$0$	$0$		$2^{13}\cdot 3^{9}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-7+\beta _{1})q^{3}-2^{5}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
42.7.c.a	$42$	$7$	42.c	7.b	$2$	$8$	$8$	$9.662$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓	✓	42.7.c.a	$2$	$0$	$0$	$0$	$0$	$-212$		$2^{9}\cdot 3^{8}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+2^{5}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
42.7.g.a	$42$	$7$	42.g	7.d	$6$	$8$	$4$	$9.662$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			42.7.g.a	$2$	$0$	$0$	$-108$	$462$	$580$		$2^{8}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(-18+9\beta _{1})q^{3}-2^{5}\beta _{1}q^{4}+\cdots$
42.7.g.b	$42$	$7$	42.g	7.d	$6$	$8$	$4$	$9.662$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			42.7.g.b	$2$	$0$	$0$	$108$	$210$	$-608$		$2^{6}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(9+9\beta _{1})q^{3}+(-2^{5}+2^{5}\beta _{1}+\cdots)q^{4}+\cdots$
42.7.h.a	$42$	$7$	42.h	21.h	$6$	$32$	$16$	$9.662$		None		✓	✓	✓	42.7.h.a	$4$	$0$	$0$	$0$	$0$	$-1684$			$\mathrm{SU}(2)[C_{6}]$
42.8.a.a	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	$\Q$	None	✓	✓	✓	✓	42.8.a.a	$1$	$0$	$-8$	$-27$	$-410$	$-343$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}-410q^{5}+\cdots$
42.8.a.b	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	$\Q$	None	✓	✓	✓	✓	42.8.a.b	$1$	$1$	$-8$	$-27$	$-18$	$343$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}-18q^{5}+6^{3}q^{6}+\cdots$
42.8.a.c	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	$\Q$	None	✓	✓	✓	✓	42.8.a.c	$1$	$1$	$-8$	$27$	$-122$	$-343$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-122q^{5}+\cdots$
42.8.a.d	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	$\Q$	None	✓	✓	✓	✓	42.8.a.d	$1$	$0$	$-8$	$27$	$270$	$343$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+270q^{5}+\cdots$
42.8.a.e	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	$\Q$	None	✓	✓	✓	✓	42.8.a.e	$1$	$0$	$8$	$-27$	$30$	$343$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+30q^{5}-6^{3}q^{6}+\cdots$
42.8.a.f	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	$\Q$	None	✓	✓	✓	✓	42.8.a.f	$1$	$0$	$8$	$27$	$470$	$-343$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+470q^{5}+\cdots$
42.8.d.a	$42$	$8$	42.d	21.c	$2$	$20$	$20$	$13.120$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	42.8.d.a	$4$	$0$	$0$	$0$	$0$	$892$		$2^{47}\cdot 3^{24}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{3}q^{3}-2^{6}q^{4}+\beta _{1}q^{5}+\cdots$
42.8.e.a	$42$	$8$	42.e	7.c	$3$	$2$	$1$	$13.120$	$\Q(\sqrt{-3}) $	None		✓			42.8.e.a	$2$	$0$	$8$	$-27$	$-165$	$-343$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(8-8\zeta_{6})q^{2}-3^{3}\zeta_{6}q^{3}-2^{6}\zeta_{6}q^{4}+\cdots$
42.8.e.b	$42$	$8$	42.e	7.c	$3$	$2$	$1$	$13.120$	$\Q(\sqrt{-3}) $	None		✓			42.8.e.b	$2$	$0$	$8$	$-27$	$290$	$1477$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(8-8\zeta_{6})q^{2}-3^{3}\zeta_{6}q^{3}-2^{6}\zeta_{6}q^{4}+\cdots$
42.8.e.c	$42$	$8$	42.e	7.c	$3$	$4$	$2$	$13.120$	$\Q(\sqrt{-3}, \sqrt{2881})$	None		✓			42.8.e.c	$2$	$0$	$-16$	$54$	$-309$	$868$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-8\beta _{1}q^{2}+(3^{3}-3^{3}\beta _{1})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots$
42.8.e.d	$42$	$8$	42.e	7.c	$3$	$6$	$3$	$13.120$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓			42.8.e.d	$2$	$0$	$-24$	$-81$	$70$	$-895$		$2^{2}\cdot 3\cdot 7$	$\mathrm{SU}(2)[C_{3}]$	$q-8\beta _{1}q^{2}+(-3^{3}+3^{3}\beta _{1})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots$

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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.