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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 67 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1827.1.b.a	$1827$	$1$	1827.b	203.c	$2$	$1$	$1$	$0.912$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-203}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+q^{4}-q^{7}+q^{16}+2q^{23}+q^{25}+\cdots$
1827.1.b.b	$1827$	$1$	1827.b	203.c	$2$	$2$	$2$	$0.912$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-87}) $	$\Q(\sqrt{609}) $		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{2}-3q^{4}+q^{7}+4iq^{8}+iq^{11}+\cdots$
1827.1.b.c	$1827$	$1$	1827.b	203.c	$2$	$4$	$4$	$0.912$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{4}q^{7}-\zeta_{12}^{3}q^{8}+\cdots$
1827.1.n.a	$1827$	$1$	1827.n	609.k	$4$	$4$	$2$	$0.912$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}q^{2}+3\zeta_{8}^{2}q^{4}-q^{7}-4\zeta_{8}^{3}q^{8}+\cdots$
1827.1.n.b	$1827$	$1$	1827.n	609.k	$4$	$4$	$2$	$0.912$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{11}-q^{16}+(-\zeta_{8}+\cdots)q^{23}+\cdots$
1827.1.bj.a	$1827$	$1$	1827.bj	203.i	$6$	$12$	$6$	$0.912$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{36}^{11}+\zeta_{36}^{13})q^{2}+(-\zeta_{36}^{4}+\cdots)q^{4}+\cdots$
1827.1.bm.a	$1827$	$1$	1827.bm	1827.am	$6$	$2$	$1$	$0.912$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-203}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1827.1.bm.b	$1827$	$1$	1827.bm	1827.am	$6$	$2$	$1$	$0.912$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-203}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1827.1.bm.c	$1827$	$1$	1827.bm	1827.am	$6$	$4$	$2$	$0.912$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-203}) $	None		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
1827.1.cl.a	$1827$	$1$	1827.cl	203.n	$14$	$6$	$1$	$0.912$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{14}^{3}+\zeta_{14}^{5})q^{2}+(-\zeta_{14}-\zeta_{14}^{3}+\cdots)q^{4}+\cdots$
1827.1.cl.b	$1827$	$1$	1827.cl	203.n	$14$	$12$	$2$	$0.912$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(\zeta_{28}^{3}+\zeta_{28}^{13})q^{2}+(-\zeta_{28}^{2}+\zeta_{28}^{6}+\cdots)q^{4}+\cdots$
1827.1.cp.a	$1827$	$1$	1827.cp	203.o	$14$	$6$	$1$	$0.912$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+(-\zeta_{14}^{5}-\zeta_{14}^{6})q^{2}+(-\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
1827.1.cp.b	$1827$	$1$	1827.cp	203.o	$14$	$12$	$2$	$0.912$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(-\zeta_{28}^{3}+\zeta_{28}^{5})q^{2}+(\zeta_{28}^{6}-\zeta_{28}^{8}+\cdots)q^{4}+\cdots$
1827.1.cw.a	$1827$	$1$	1827.cw	609.aj	$28$	$24$	$2$	$0.912$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+(\zeta_{56}^{19}-\zeta_{56}^{27})q^{2}+(-\zeta_{56}^{10}+\cdots)q^{4}+\cdots$
1827.1.cw.b	$1827$	$1$	1827.cw	609.aj	$28$	$24$	$2$	$0.912$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q+(\zeta_{56}^{19}+\zeta_{56}^{27})q^{2}+(-\zeta_{56}^{10}+\cdots)q^{4}+\cdots$
1827.2.a.a	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+q^{7}+3q^{8}+2q^{10}+\cdots$
1827.2.a.b	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-6q^{13}-q^{14}+\cdots$
1827.2.a.c	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots$
1827.2.a.d	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots$
1827.2.a.e	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+4q^{5}+q^{7}+8q^{10}+\cdots$
1827.2.a.f	$1827$	$2$	1827.a	1.a	$1$	$2$	$2$	$14.589$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-4$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-2\beta q^{5}-q^{7}+4\beta q^{10}+\cdots$
1827.2.a.g	$1827$	$2$	1827.a	1.a	$1$	$2$	$2$	$14.589$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+(-2+\beta )q^{5}-q^{7}-3q^{8}+\cdots$
1827.2.a.h	$1827$	$2$	1827.a	1.a	$1$	$2$	$2$	$14.589$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2+\beta )q^{5}+\cdots$
1827.2.a.i	$1827$	$2$	1827.a	1.a	$1$	$3$	$3$	$14.589$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1827.2.a.j	$1827$	$2$	1827.a	1.a	$1$	$3$	$3$	$14.589$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-\beta _{1}-\beta _{2})q^{5}+\cdots$
1827.2.a.k	$1827$	$2$	1827.a	1.a	$1$	$3$	$3$	$14.589$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
1827.2.a.l	$1827$	$2$	1827.a	1.a	$1$	$4$	$4$	$14.589$	4.4.4352.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}+\beta _{3})q^{2}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1827.2.a.m	$1827$	$2$	1827.a	1.a	$1$	$4$	$4$	$14.589$	4.4.6224.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots$
1827.2.a.n	$1827$	$2$	1827.a	1.a	$1$	$4$	$4$	$14.589$	4.4.14656.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
1827.2.a.o	$1827$	$2$	1827.a	1.a	$1$	$5$	$5$	$14.589$	5.5.2626356.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$-5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{4})q^{5}+\cdots$
1827.2.a.p	$1827$	$2$	1827.a	1.a	$1$	$5$	$5$	$14.589$	5.5.1280720.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$4$	$-5$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots$
1827.2.a.q	$1827$	$2$	1827.a	1.a	$1$	$7$	$7$	$14.589$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-5$	$0$	$-8$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1827.2.a.r	$1827$	$2$	1827.a	1.a	$1$	$7$	$7$	$14.589$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-8$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
1827.2.a.s	$1827$	$2$	1827.a	1.a	$1$	$7$	$7$	$14.589$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$8$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6})q^{4}+(1+\cdots)q^{5}+\cdots$
1827.2.a.t	$1827$	$2$	1827.a	1.a	$1$	$7$	$7$	$14.589$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$0$	$8$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
1827.2.d.a	$1827$	$2$	1827.d	21.c	$2$	$72$	$72$	$14.589$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
1827.2.e.a	$1827$	$2$	1827.e	29.b	$2$	$2$	$2$	$14.589$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}-2q^{5}-q^{7}-2\beta q^{11}-6q^{13}+\cdots$
1827.2.e.b	$1827$	$2$	1827.e	29.b	$2$	$6$	$6$	$14.589$	6.0.16516096.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(-1+\beta _{3})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
1827.2.e.c	$1827$	$2$	1827.e	29.b	$2$	$6$	$6$	$14.589$	6.0.25809920.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$-6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{4})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots$
1827.2.e.d	$1827$	$2$	1827.e	29.b	$2$	$12$	$12$	$14.589$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$12$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{3}q^{4}+\beta _{1}q^{5}+q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots$
1827.2.e.e	$1827$	$2$	1827.e	29.b	$2$	$14$	$14$	$14.589$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-14$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{8}q^{5}-q^{7}+\cdots$
1827.2.e.f	$1827$	$2$	1827.e	29.b	$2$	$16$	$16$	$14.589$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-16$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-1+\beta _{1})q^{4}+\beta _{4}q^{5}-q^{7}+\cdots$
1827.2.e.g	$1827$	$2$	1827.e	29.b	$2$	$18$	$18$	$14.589$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$18$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{5}q^{5}+q^{7}+\cdots$
1827.2.h.a	$1827$	$2$	1827.h	609.h	$2$	$8$	$8$	$14.589$	8.0.157351936.1	$_{}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{6}q^{2}+(2-\beta _{3})q^{4}-\beta _{3}q^{7}+(-\beta _{5}+\cdots)q^{8}+\cdots$
1827.2.h.b	$1827$	$2$	1827.h	609.h	$2$	$72$	$72$	$14.589$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
1827.4.a.a	$1827$	$4$	1827.a	1.a	$1$	$1$	$1$	$107.796$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-5$	$0$	$-4$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}+17q^{4}-4q^{5}+7q^{7}-45q^{8}+\cdots$
1827.4.a.b	$1827$	$4$	1827.a	1.a	$1$	$1$	$1$	$107.796$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-4$	$0$	$-2$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+8q^{4}-2q^{5}+7q^{7}+8q^{10}+\cdots$
1827.4.a.c	$1827$	$4$	1827.a	1.a	$1$	$1$	$1$	$107.796$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-14$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}-14q^{5}+7q^{7}+15q^{8}+\cdots$
1827.4.a.d	$1827$	$4$	1827.a	1.a	$1$	$1$	$1$	$107.796$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$-1$	$0$	$-12$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}-12q^{5}+7q^{7}+15q^{8}+\cdots$
1827.4.a.e	$1827$	$4$	1827.a	1.a	$1$	$1$	$1$	$107.796$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$12$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-7q^{4}+12q^{5}+7q^{7}-15q^{8}+\cdots$

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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.