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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 127 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
924.1.z.a	$924$	$1$	924.z	924.z	$6$	$2$	$1$	$0.461$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-33}) $	None		✓			924.1.z.a	$4$	$0$	$-1$	$-1$	$0$	$2$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+q^{6}+\cdots$
924.1.z.b	$924$	$1$	924.z	924.z	$6$	$2$	$1$	$0.461$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-33}) $	None		✓			924.1.z.a	$4$	$0$	$-1$	$1$	$0$	$-2$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-q^{6}+\cdots$
924.1.z.c	$924$	$1$	924.z	924.z	$6$	$2$	$1$	$0.461$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-33}) $	None		✓			924.1.z.a	$4$	$0$	$1$	$-1$	$0$	$-2$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-q^{6}+\cdots$
924.1.z.d	$924$	$1$	924.z	924.z	$6$	$2$	$1$	$0.461$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-33}) $	None		✓			924.1.z.a	$4$	$0$	$1$	$1$	$0$	$2$		$1$		$q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+q^{6}+\cdots$
924.1.bk.a	$924$	$1$	924.bk	924.ak	$10$	$4$	$1$	$0.461$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		✓			924.1.bk.a	$4$	$0$	$-1$	$-1$	$3$	$-1$		$1$		$q-\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(1+\cdots)q^{5}+\cdots$
924.1.bk.b	$924$	$1$	924.bk	924.ak	$10$	$4$	$1$	$0.461$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		✓			924.1.bk.a	$4$	$0$	$-1$	$1$	$-3$	$1$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
924.1.bk.c	$924$	$1$	924.bk	924.ak	$10$	$4$	$1$	$0.461$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		✓			924.1.bk.a	$4$	$0$	$1$	$-1$	$-3$	$-1$		$1$		$q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
924.1.bk.d	$924$	$1$	924.bk	924.ak	$10$	$4$	$1$	$0.461$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		✓			924.1.bk.a	$4$	$0$	$1$	$1$	$3$	$1$		$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(1+\cdots)q^{5}+\cdots$
924.2.a.a	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	924.2.a.a	$1$	$0$	$0$	$-1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
924.2.a.b	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	924.2.a.b	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
924.2.a.c	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	924.2.a.c	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-3q^{13}+\cdots$
924.2.a.d	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	924.2.a.d	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
924.2.a.e	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	924.2.a.e	$1$	$1$	$0$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}+3q^{13}+\cdots$
924.2.a.f	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	924.2.a.f	$1$	$1$	$0$	$1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}-7q^{13}+\cdots$
924.2.a.g	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	924.2.a.g	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
924.2.a.h	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	924.2.a.h	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
924.2.c.a	$924$	$2$	924.c	28.d	$2$	$40$	$40$	$7.378$		$_{}$	None	None		✓			924.2.c.a	$2$	$0$	$0$	$-40$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
924.2.c.b	$924$	$2$	924.c	28.d	$2$	$40$	$40$	$7.378$		$_{}$	None	None		✓			924.2.c.a	$2$	$0$	$0$	$40$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
924.2.d.a	$924$	$2$	924.d	33.d	$2$	$8$	$8$	$7.378$	8.0.2702336256.1	$_{}$	None	None		✓			924.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{5}q^{7}-3q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
924.2.d.b	$924$	$2$	924.d	33.d	$2$	$16$	$16$	$7.378$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		924.2.d.b	$4$	$0$	$0$	$2$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}-\beta _{5}q^{5}-\beta _{8}q^{7}+(1-\beta _{9}+\cdots)q^{9}+\cdots$
924.2.f.a	$924$	$2$	924.f	12.b	$2$	$60$	$60$	$7.378$		$_{}$	None	None		✓			924.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
924.2.f.b	$924$	$2$	924.f	12.b	$2$	$60$	$60$	$7.378$		$_{}$	None	None		✓			924.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
924.2.i.a	$924$	$2$	924.i	77.b	$2$	$4$	$4$	$7.378$	$\Q(i, \sqrt{7})$	$_{}$	None	None		✓			924.2.i.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}-q^{9}+(2+\cdots)q^{11}+\cdots$
924.2.i.b	$924$	$2$	924.i	77.b	$2$	$12$	$12$	$7.378$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		924.2.i.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{3}+(\beta _{4}+\beta _{6})q^{5}-\beta _{3}q^{7}-q^{9}+\cdots$
924.2.k.a	$924$	$2$	924.k	44.c	$2$	$4$	$4$	$7.378$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			924.2.k.a	$2$	$0$	$-4$	$0$	$4$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{2}-\beta _{1}q^{3}+2\beta _{1}q^{4}+\cdots$
924.2.k.b	$924$	$2$	924.k	44.c	$2$	$4$	$4$	$7.378$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			924.2.k.a	$2$	$0$	$4$	$0$	$4$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{2}-\beta _{1}q^{3}+2\beta _{1}q^{4}+(1+\cdots)q^{5}+\cdots$
924.2.k.c	$924$	$2$	924.k	44.c	$2$	$32$	$32$	$7.378$		$_{}$	None	None		✓			924.2.k.c	$2$	$0$	$-6$	$0$	$-4$	$-32$			$\mathrm{SU}(2)[C_{2}]$
924.2.k.d	$924$	$2$	924.k	44.c	$2$	$32$	$32$	$7.378$		$_{}$	None	None		✓			924.2.k.c	$2$	$0$	$6$	$0$	$-4$	$32$			$\mathrm{SU}(2)[C_{2}]$
924.2.l.a	$924$	$2$	924.l	21.c	$2$	$4$	$4$	$7.378$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			924.2.l.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(-1+\beta _{1}+\beta _{3})q^{7}-3\beta _{2}q^{9}+\cdots$
924.2.l.b	$924$	$2$	924.l	21.c	$2$	$4$	$4$	$7.378$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			924.2.l.b	$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{3} q^{3}-\beta_{3} q^{5}+(\beta_{2}+2)q^{7}+3 q^{9}+\cdots$
924.2.l.c	$924$	$2$	924.l	21.c	$2$	$8$	$8$	$7.378$	8.0.342102016.5	$_{}$	None	None		✓			924.2.l.c	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{5}+\beta _{6})q^{3}+(-\beta _{2}+\beta _{4}-\beta _{5})q^{5}+\cdots$
924.2.l.d	$924$	$2$	924.l	21.c	$2$	$12$	$12$	$7.378$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		924.2.l.d	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}+(-\beta _{8}-\beta _{10})q^{5}+(-\beta _{7}+\cdots)q^{7}+\cdots$
924.2.n.a	$924$	$2$	924.n	924.n	$2$	$8$	$8$	$7.378$	8.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-21}) $	None		✓			924.2.n.a	$16$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-\beta _{3}q^{3}-2q^{4}+(-\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots$
924.2.n.b	$924$	$2$	924.n	924.n	$2$	$8$	$8$	$7.378$	8.0.3317760000.6	$_{}$	None	None		✓			924.2.n.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{2}-\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots$
924.2.n.c	$924$	$2$	924.n	924.n	$2$	$8$	$8$	$7.378$	8.0.3317760000.6	$_{}$	None	None		✓			924.2.n.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots$
924.2.n.d	$924$	$2$	924.n	924.n	$2$	$8$	$8$	$7.378$	8.0.$\cdots$.7	$_{}$	$\Q(\sqrt{-33}) $	None		✓			924.2.n.d	$16$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{5}q^{2}+\beta _{1}q^{3}+2q^{4}-\beta _{3}q^{6}+\beta _{6}q^{7}+\cdots$
924.2.n.e	$924$	$2$	924.n	924.n	$2$	$16$	$16$	$7.378$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-77}) $	None		✓			924.2.n.e	$16$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-\beta _{13}q^{3}-2q^{4}+\beta _{4}q^{6}+\cdots$
924.2.n.f	$924$	$2$	924.n	924.n	$2$	$24$	$24$	$7.378$		$_{}$	$\Q(\sqrt{-231}) $	None		✓			924.2.n.f	$16$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{2}]$
924.2.n.g	$924$	$2$	924.n	924.n	$2$	$112$	$112$	$7.378$		$_{}$	None	None		✓	✓		924.2.n.g	$16$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
924.2.q.a	$924$	$2$	924.q	7.c	$3$	$2$	$1$	$7.378$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			924.2.q.a	$2$	$0$	$0$	$-1$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$
924.2.q.b	$924$	$2$	924.q	7.c	$3$	$2$	$1$	$7.378$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			924.2.q.b	$2$	$0$	$0$	$1$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
924.2.q.c	$924$	$2$	924.q	7.c	$3$	$2$	$1$	$7.378$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			924.2.q.c	$2$	$0$	$0$	$1$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
924.2.q.d	$924$	$2$	924.q	7.c	$3$	$4$	$2$	$7.378$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			924.2.q.d	$2$	$0$	$0$	$-2$	$0$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1})q^{3}+(1-\beta _{2})q^{7}+\beta _{1}q^{9}+\cdots$
924.2.q.e	$924$	$2$	924.q	7.c	$3$	$8$	$4$	$7.378$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			924.2.q.e	$2$	$0$	$0$	$4$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{3}-\beta _{4}q^{5}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
924.2.q.f	$924$	$2$	924.q	7.c	$3$	$10$	$5$	$7.378$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓		924.2.q.f	$2$	$0$	$0$	$-5$	$0$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{3}+(\beta _{4}-\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
924.2.r.a	$924$	$2$	924.r	11.c	$5$	$4$	$1$	$7.378$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			924.2.r.a	$2$	$1$	$0$	$-1$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+(-2+2\zeta_{10}-2\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
924.2.r.b	$924$	$2$	924.r	11.c	$5$	$4$	$1$	$7.378$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			924.2.r.b	$2$	$0$	$0$	$-1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+\zeta_{10}^{3}q^{7}+\cdots$
924.2.r.c	$924$	$2$	924.r	11.c	$5$	$4$	$1$	$7.378$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			924.2.r.c	$2$	$0$	$0$	$1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+(-1+2\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
924.2.r.d	$924$	$2$	924.r	11.c	$5$	$4$	$1$	$7.378$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			924.2.r.d	$2$	$0$	$0$	$1$	$6$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+(2+2\zeta_{10}^{2})q^{5}-\zeta_{10}^{3}q^{7}+\cdots$
924.2.r.e	$924$	$2$	924.r	11.c	$5$	$16$	$4$	$7.378$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			924.2.r.e	$2$	$0$	$0$	$-4$	$-5$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{9}q^{3}+(-1-\beta _{2}-\beta _{3}+\beta _{9}-\beta _{11}+\cdots)q^{5}+\cdots$

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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.