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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 75 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
828.1.j.a	$828$	$1$	828.j	828.j	$6$	$6$	$3$	$0.413$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		✓			828.1.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}q^{3}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{5}q^{6}+\cdots$
828.1.j.b	$828$	$1$	828.j	828.j	$6$	$6$	$3$	$0.413$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		✓			828.1.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{2}q^{2}-\zeta_{18}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$
828.2.a.a	$828$	$2$	828.a	1.a	$1$	$1$	$1$	$6.612$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	828.2.a.a	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots$
828.2.a.b	$828$	$2$	828.a	1.a	$1$	$1$	$1$	$6.612$	$\Q$	$_{}$	None	None	✓				92.2.a.b	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-q^{13}+6q^{17}+2q^{19}+q^{23}+\cdots$
828.2.a.c	$828$	$2$	828.a	1.a	$1$	$1$	$1$	$6.612$	$\Q$	$_{}$	None	None	✓				92.2.a.a	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-2q^{11}-5q^{13}-4q^{17}+\cdots$
828.2.a.d	$828$	$2$	828.a	1.a	$1$	$1$	$1$	$6.612$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	828.2.a.a	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}+4q^{11}-2q^{13}+2q^{17}+\cdots$
828.2.a.e	$828$	$2$	828.a	1.a	$1$	$2$	$2$	$6.612$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		276.2.a.b	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}-\beta q^{7}-4\beta q^{11}+4\beta q^{13}+\cdots$
828.2.a.f	$828$	$2$	828.a	1.a	$1$	$2$	$2$	$6.612$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓		✓		276.2.a.a	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(2+\beta )q^{7}+4q^{13}+(-4-\beta )q^{17}+\cdots$
828.2.c.a	$828$	$2$	828.c	12.b	$2$	$2$	$2$	$6.612$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			828.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}+2\beta q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots$
828.2.c.b	$828$	$2$	828.c	12.b	$2$	$2$	$2$	$6.612$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			828.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}+2\beta q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots$
828.2.c.c	$828$	$2$	828.c	12.b	$2$	$8$	$8$	$6.612$	8.0.18939904.2	$_{}$	None	None		✓			828.2.c.c	$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots$
828.2.c.d	$828$	$2$	828.c	12.b	$2$	$8$	$8$	$6.612$	8.0.18939904.2	$_{}$	None	None		✓			828.2.c.c	$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{3})q^{2}+(\beta _{2}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
828.2.c.e	$828$	$2$	828.c	12.b	$2$	$12$	$12$	$6.612$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			828.2.c.e	$2$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{8})q^{4}+(-\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots$
828.2.c.f	$828$	$2$	828.c	12.b	$2$	$12$	$12$	$6.612$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			828.2.c.e	$2$	$0$	$4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+(\beta _{2}+\beta _{7})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
828.2.e.a	$828$	$2$	828.e	92.b	$2$	$4$	$4$	$6.612$	$\Q(i, \sqrt{14})$	$_{}$	None	None					92.2.b.a	$4$	$0$	$4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots$
828.2.e.b	$828$	$2$	828.e	92.b	$2$	$6$	$6$	$6.612$	6.0.8869743.1	$_{}$	$\Q(\sqrt{-23}) $	None					92.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{5}q^{2}+\beta _{3}q^{4}+(2-\beta _{2})q^{8}+(\beta _{1}+\cdots)q^{13}+\cdots$
828.2.e.c	$828$	$2$	828.e	92.b	$2$	$8$	$8$	$6.612$	8.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-69}) $	None		✓			828.2.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-2q^{4}-\beta _{4}q^{5}-\beta _{5}q^{7}-2\beta _{2}q^{8}+\cdots$
828.2.e.d	$828$	$2$	828.e	92.b	$2$	$8$	$8$	$6.612$	8.0.3317760000.6	$_{}$	None	None		✓			828.2.e.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{4}+\beta _{6}q^{7}+(-\beta _{1}-2\beta _{7})q^{8}+\cdots$
828.2.e.e	$828$	$2$	828.e	92.b	$2$	$8$	$8$	$6.612$	8.0.157351936.1	$_{}$	None	None		✓			828.2.e.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}+\beta _{3})q^{2}+(2-\beta _{1})q^{4}-2\beta _{6}q^{5}+\cdots$
828.2.e.f	$828$	$2$	828.e	92.b	$2$	$24$	$24$	$6.612$		$_{}$	None	None			✓		276.2.e.a	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
828.2.g.a	$828$	$2$	828.g	69.c	$2$	$8$	$8$	$6.612$	8.0.$\cdots$.6	$_{}$	None	None		✓	✓	✓	828.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{5}-\beta _{5}q^{7}+\beta _{2}q^{11}+(-1-\beta _{3}+\cdots)q^{13}+\cdots$
828.2.i.a	$828$	$2$	828.i	9.c	$3$	$6$	$3$	$6.612$	6.0.309123.1	$_{}$	None	None		✓			828.2.i.a	$2$	$0$	$0$	$-2$	$2$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
828.2.i.b	$828$	$2$	828.i	9.c	$3$	$10$	$5$	$6.612$	10.0.$\cdots$.1	$_{}$	None	None		✓			828.2.i.b	$2$	$0$	$0$	$3$	$6$	$-3$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-\beta _{2}+\beta _{3}-\beta _{7})q^{5}+(-1+\cdots)q^{7}+\cdots$
828.2.i.c	$828$	$2$	828.i	9.c	$3$	$12$	$6$	$6.612$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			828.2.i.c	$2$	$0$	$0$	$-2$	$-6$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{11})q^{3}+(1-\beta _{3}+\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots$
828.2.i.d	$828$	$2$	828.i	9.c	$3$	$16$	$8$	$6.612$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		828.2.i.d	$2$	$0$	$0$	$3$	$-2$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{7}q^{3}+(\beta _{4}-\beta _{6}-\beta _{9}+\beta _{12})q^{5}+\cdots$
828.2.k.a	$828$	$2$	828.k	207.g	$6$	$48$	$24$	$6.612$		$_{}$	None	None		✓	✓	✓	828.2.k.a	$4$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
828.2.m.a	$828$	$2$	828.m	828.m	$6$	$8$	$4$	$6.612$	8.0.303595776.1	$_{}$	None	None		✓			828.2.m.a	$8$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{3}+\beta _{4})q^{2}+(\beta _{3}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots$
828.2.m.b	$828$	$2$	828.m	828.m	$6$	$12$	$6$	$6.612$	12.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-23}) $	None		✓			828.2.m.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-\beta _{11}q^{2}+(\beta _{3}-\beta _{10})q^{3}+(-\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots$
828.2.m.c	$828$	$2$	828.m	828.m	$6$	$12$	$6$	$6.612$	12.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-23}) $	None		✓			828.2.m.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{2}q^{2}-\beta _{5}q^{3}+(\beta _{8}-\beta _{9})q^{4}+\beta _{7}q^{6}+\cdots$
828.2.m.d	$828$	$2$	828.m	828.m	$6$	$248$	$124$	$6.612$		$_{}$	None	None		✓	✓		828.2.m.d	$8$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
828.2.o.a	$828$	$2$	828.o	36.h	$6$	$132$	$66$	$6.612$		$_{}$	None	None		✓			828.2.o.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
828.2.o.b	$828$	$2$	828.o	36.h	$6$	$132$	$66$	$6.612$		$_{}$	None	None		✓			828.2.o.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
828.2.q.a	$828$	$2$	828.q	23.c	$11$	$20$	$2$	$6.612$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None					92.2.e.a	$2$	$0$	$0$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\beta _{2}+\beta _{10}+\beta _{11}+\beta _{13}-\beta _{15}+\cdots)q^{5}+\cdots$
828.2.q.b	$828$	$2$	828.q	23.c	$11$	$20$	$2$	$6.612$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None					276.2.i.b	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\beta _{6}+\beta _{7}+\beta _{8}-\beta _{14}-\beta _{17})q^{5}+\cdots$
828.2.q.c	$828$	$2$	828.q	23.c	$11$	$20$	$2$	$6.612$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None					276.2.i.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1-\beta _{8}-\beta _{9}-\beta _{10}+\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots$
828.2.q.d	$828$	$2$	828.q	23.c	$11$	$40$	$4$	$6.612$		$_{}$	None	None		✓	✓		828.2.q.d	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{11}]$
828.2.s.a	$828$	$2$	828.s	69.g	$22$	$80$	$8$	$6.612$		$_{}$	None	None		✓	✓	✓	828.2.s.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
828.2.u.a	$828$	$2$	828.u	92.h	$22$	$100$	$10$	$6.612$		$_{}$	None	None					92.2.h.a	$4$	$0$	$7$	$0$	$22$	$0$			$\mathrm{SU}(2)[C_{22}]$
828.2.u.b	$828$	$2$	828.u	92.h	$22$	$240$	$24$	$6.612$		$_{}$	None	None		✓			828.2.u.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
828.2.u.c	$828$	$2$	828.u	92.h	$22$	$240$	$24$	$6.612$		$_{}$	None	None					276.2.m.a	$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
828.2.w.a	$828$	$2$	828.w	276.o	$22$	$480$	$48$	$6.612$		$_{}$	None	None		✓	✓	✓	828.2.w.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
828.2.y.a	$828$	$2$	828.y	207.m	$33$	$480$	$24$	$6.612$		$_{}$	None	None		✓	✓	✓	828.2.y.a	$4$	$0$	$0$	$-2$	$6$	$0$			$\mathrm{SU}(2)[C_{33}]$
828.2.ba.a	$828$	$2$	828.ba	828.aa	$66$	$2800$	$140$	$6.612$		$_{}$	None	None		✓	✓	✓	828.2.ba.a	$8$	$0$	$-27$	$0$	$-54$	$0$			$\mathrm{SU}(2)[C_{66}]$
828.2.bc.a	$828$	$2$	828.bc	828.ac	$66$	$2800$	$140$	$6.612$		$_{}$	None	None		✓	✓	✓	828.2.bc.a	$8$	$0$	$-9$	$0$	$-22$	$0$			$\mathrm{SU}(2)[C_{66}]$
828.2.be.a	$828$	$2$	828.be	207.o	$66$	$480$	$24$	$6.612$		$_{}$	None	None		✓	✓	✓	828.2.be.a	$4$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{66}]$
828.3.b.a	$828$	$3$	828.b	23.b	$2$	$4$	$4$	$22.561$	4.0.53792.1	$_{}$	None	None					92.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
828.3.b.b	$828$	$3$	828.b	23.b	$2$	$8$	$8$	$22.561$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None					276.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(\beta _{2}+\beta _{7})q^{7}+(\beta _{2}+\beta _{6})q^{11}+\cdots$
828.3.b.c	$828$	$3$	828.b	23.b	$2$	$8$	$8$	$22.561$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			828.3.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{5}-\beta _{5}q^{7}-\beta _{3}q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots$
828.3.d.a	$828$	$3$	828.d	3.b	$2$	$16$	$16$	$22.561$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	828.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{11}q^{7}-\beta _{6}q^{11}+(-1+\cdots)q^{13}+\cdots$
828.3.h.a	$828$	$3$	828.h	276.h	$2$	$96$	$96$	$22.561$		$_{}$	None	None		✓	✓	✓	828.3.h.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.