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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 122 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
464.1.h.a	$464$	$1$	464.h	116.d	$2$	$1$	$1$	$0.232$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{29}) $	✓	✓			464.1.h.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+2q^{5}-q^{9}-2q^{13}+3q^{25}-q^{29}+\cdots$
464.1.h.b	$464$	$1$	464.h	116.d	$2$	$2$	$2$	$0.232$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None	✓	✓	✓		464.1.h.b	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{3}-q^{5}+2q^{9}+\beta q^{11}+q^{13}+\cdots$
464.1.v.a	$464$	$1$	464.v	116.h	$14$	$6$	$1$	$0.232$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	464.1.v.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-\zeta_{14}-\zeta_{14}^{3})q^{5}-\zeta_{14}^{6}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots$
464.2.a.a	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	$\Q$	$_{}$	None	None	✓				116.2.a.c	$1$	$0$	$0$	$-2$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots$
464.2.a.b	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	$\Q$	$_{}$	None	None	✓				232.2.a.b	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}-2q^{9}-3q^{11}+\cdots$
464.2.a.c	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	$\Q$	$_{}$	None	None	✓				116.2.a.b	$1$	$0$	$0$	$-1$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+4q^{7}-2q^{9}-3q^{11}+\cdots$
464.2.a.d	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	$\Q$	$_{}$	None	None	✓				232.2.a.a	$1$	$1$	$0$	$1$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-2q^{7}-2q^{9}+3q^{11}+\cdots$
464.2.a.e	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	$\Q$	$_{}$	None	None	✓				58.2.a.b	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots$
464.2.a.f	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	$\Q$	$_{}$	None	None	✓				58.2.a.a	$1$	$0$	$0$	$3$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{5}+2q^{7}+6q^{9}+q^{11}+\cdots$
464.2.a.g	$464$	$2$	464.a	1.a	$1$	$1$	$1$	$3.705$	$\Q$	$_{}$	None	None	✓				116.2.a.a	$1$	$0$	$0$	$3$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+3q^{5}-4q^{7}+6q^{9}+q^{11}+\cdots$
464.2.a.h	$464$	$2$	464.a	1.a	$1$	$2$	$2$	$3.705$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓	✓	29.2.a.a	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}-2\beta q^{7}-2\beta q^{9}+\cdots$
464.2.a.i	$464$	$2$	464.a	1.a	$1$	$2$	$2$	$3.705$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				232.2.a.c	$1$	$0$	$0$	$2$	$-2$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1+2\beta )q^{5}+4q^{7}+\cdots$
464.2.a.j	$464$	$2$	464.a	1.a	$1$	$3$	$3$	$3.705$	3.3.568.1	$_{}$	None	None	✓		✓		232.2.a.d	$1$	$0$	$0$	$-2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots$
464.2.e.a	$464$	$2$	464.e	29.b	$2$	$2$	$2$	$3.705$	$\Q(\sqrt{-5}) $	$_{}$	None	None					29.2.b.a	$2$	$1$	$0$	$0$	$-6$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-3q^{5}-2q^{7}-2q^{9}-\beta q^{11}+\cdots$
464.2.e.b	$464$	$2$	464.e	29.b	$2$	$2$	$2$	$3.705$	$\Q(\sqrt{-7}) $	$_{}$	None	None					116.2.c.a	$2$	$0$	$0$	$0$	$2$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+q^{5}+2q^{7}-4q^{9}-\beta q^{11}+\cdots$
464.2.e.c	$464$	$2$	464.e	29.b	$2$	$2$	$2$	$3.705$	$\Q(\sqrt{-1}) $	$_{}$	None	None					58.2.b.a	$2$	$0$	$0$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+q^{5}+2 q^{7}+2 q^{9}-5 i q^{11}+\cdots$
464.2.e.d	$464$	$2$	464.e	29.b	$2$	$8$	$8$	$3.705$	8.0.4589249536.2	$_{}$	None	None			✓		232.2.e.a	$2$	$0$	$0$	$0$	$2$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{4}q^{5}+(-1+\beta _{6})q^{7}+(-1+\cdots)q^{9}+\cdots$
464.2.j.a	$464$	$2$	464.j	464.j	$4$	$116$	$58$	$3.705$		$_{}$	None	None		✓	✓	✓	464.2.j.a	$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
464.2.k.a	$464$	$2$	464.k	116.e	$4$	$2$	$1$	$3.705$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			464.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q-4 i q^{5}+3 i q^{9}-6 i q^{13}+(-3 i-3)q^{17}+\cdots$
464.2.k.b	$464$	$2$	464.k	116.e	$4$	$8$	$4$	$3.705$	8.0.1024000000.2	$_{}$	None	None		✓			464.2.k.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{5})q^{7}+\cdots$
464.2.k.c	$464$	$2$	464.k	116.e	$4$	$20$	$10$	$3.705$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		464.2.k.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{13}q^{3}+\beta _{18}q^{5}+\beta _{9}q^{7}+(\beta _{1}-\beta _{8}+\cdots)q^{9}+\cdots$
464.2.m.a	$464$	$2$	464.m	464.m	$4$	$2$	$1$	$3.705$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			464.2.m.a	$2$	$0$	$-2$	$2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+(i+1)q^{3}+2 i q^{4}+\cdots$
464.2.m.b	$464$	$2$	464.m	464.m	$4$	$2$	$1$	$3.705$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			464.2.m.a	$2$	$0$	$2$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+(-i-1)q^{3}+2 i q^{4}+\cdots$
464.2.m.c	$464$	$2$	464.m	464.m	$4$	$112$	$56$	$3.705$		$_{}$	None	None		✓	✓		464.2.m.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
464.2.n.a	$464$	$2$	464.n	16.e	$4$	$112$	$56$	$3.705$		$_{}$	None	None		✓	✓	✓	464.2.n.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
464.2.t.a	$464$	$2$	464.t	464.t	$4$	$116$	$58$	$3.705$		$_{}$	None	None		✓	✓	✓	464.2.j.a	$2$	$0$	$-4$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
464.2.u.a	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	$_{}$	None	None					232.2.m.c	$2$	$0$	$0$	$-5$	$7$	$3$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots$
464.2.u.b	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	$_{}$	None	None					58.2.d.a	$2$	$0$	$0$	$-3$	$-4$	$5$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{3}+\cdots$
464.2.u.c	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	$_{}$	None	None					116.2.g.a	$2$	$0$	$0$	$-3$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-2\zeta_{14}+2\zeta_{14}^{2}-2\zeta_{14}^{3}+2\zeta_{14}^{4}+\cdots)q^{3}+\cdots$
464.2.u.d	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	$_{}$	None	None					232.2.m.b	$2$	$0$	$0$	$1$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1+2\zeta_{14}^{2}-2\zeta_{14}^{3}-\zeta_{14}^{5})q^{3}+\cdots$
464.2.u.e	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	$_{}$	None	None					232.2.m.a	$2$	$0$	$0$	$3$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+(\zeta_{14}^{3}+\cdots)q^{5}+\cdots$
464.2.u.f	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	$_{}$	None	None					29.2.d.a	$2$	$0$	$0$	$5$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{3}+\cdots)q^{5}+\cdots$
464.2.u.g	$464$	$2$	464.u	29.d	$7$	$12$	$2$	$3.705$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					116.2.g.b	$2$	$0$	$0$	$3$	$-1$	$7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(\beta _{1}+\beta _{8})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
464.2.u.h	$464$	$2$	464.u	29.d	$7$	$12$	$2$	$3.705$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					58.2.d.b	$2$	$0$	$0$	$3$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{11}q^{3}+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots$
464.2.u.i	$464$	$2$	464.u	29.d	$7$	$24$	$4$	$3.705$		$_{}$	None	None			✓		232.2.m.d	$2$	$0$	$0$	$1$	$-8$	$-5$			$\mathrm{SU}(2)[C_{7}]$
464.2.y.a	$464$	$2$	464.y	29.e	$14$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	$_{}$	None	None					116.2.i.b	$2$	$0$	$0$	$-7$	$-1$	$5$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-1-\zeta_{14}^{3})q^{3}+(1-2\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{5}+\cdots$
464.2.y.b	$464$	$2$	464.y	29.e	$14$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	$_{}$	None	None					116.2.i.a	$2$	$0$	$0$	$7$	$-1$	$-9$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(1+\zeta_{14}^{3})q^{3}+(-1-\zeta_{14}^{2}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots$
464.2.y.c	$464$	$2$	464.y	29.e	$14$	$12$	$2$	$3.705$	$\Q(\zeta_{28})$	$_{}$	None	None					58.2.e.a	$2$	$0$	$0$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(\zeta_{28}-\zeta_{28}^{5}+\zeta_{28}^{11})q^{3}+(2\zeta_{28}+\cdots)q^{5}+\cdots$
464.2.y.d	$464$	$2$	464.y	29.e	$14$	$12$	$2$	$3.705$	12.0.$\cdots$.1	$_{}$	None	None					29.2.e.a	$2$	$0$	$0$	$7$	$-1$	$11$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(2+\beta _{1}+\beta _{5}+\beta _{7}+\beta _{8}-\beta _{9})q^{3}+\cdots$
464.2.y.e	$464$	$2$	464.y	29.e	$14$	$48$	$8$	$3.705$		$_{}$	None	None			✓		232.2.q.a	$2$	$0$	$0$	$0$	$-2$	$4$			$\mathrm{SU}(2)[C_{14}]$
464.2.bc.a	$464$	$2$	464.bc	464.ac	$28$	$696$	$58$	$3.705$		$_{}$	None	None		✓	✓	✓	464.2.bc.a	$2$	$0$	$-10$	$-10$	$-14$	$-20$			$\mathrm{SU}(2)[C_{28}]$
464.2.bi.a	$464$	$2$	464.bi	464.ai	$28$	$696$	$58$	$3.705$		$_{}$	None	None		✓	✓	✓	464.2.bi.a	$4$	$0$	$-10$	$-10$	$-10$	$0$			$\mathrm{SU}(2)[C_{28}]$
464.2.bj.a	$464$	$2$	464.bj	464.aj	$28$	$696$	$58$	$3.705$		$_{}$	None	None		✓	✓	✓	464.2.bj.a	$4$	$0$	$-14$	$-14$	$-10$	$0$			$\mathrm{SU}(2)[C_{28}]$
464.2.bl.a	$464$	$2$	464.bl	116.l	$28$	$12$	$1$	$3.705$	$\Q(\zeta_{28})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			464.2.bl.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{28}]$	$q+(1-\zeta_{28}^{2}+2\zeta_{28}^{4}+2\zeta_{28}^{5}-\zeta_{28}^{6}+\cdots)q^{5}+\cdots$
464.2.bl.b	$464$	$2$	464.bl	116.l	$28$	$48$	$4$	$3.705$		$_{}$	None	None		✓			464.2.bl.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
464.2.bl.c	$464$	$2$	464.bl	116.l	$28$	$120$	$10$	$3.705$		$_{}$	None	None		✓	✓		464.2.bl.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
464.2.bm.a	$464$	$2$	464.bm	464.am	$28$	$696$	$58$	$3.705$		$_{}$	None	None		✓	✓	✓	464.2.bc.a	$2$	$0$	$-14$	$-14$	$-14$	$-20$			$\mathrm{SU}(2)[C_{28}]$
464.3.d.a	$464$	$3$	464.d	4.b	$2$	$8$	$8$	$12.643$	8.0.$\cdots$.2	$_{}$	None	None		✓			464.3.d.a	$2$	$0$	$0$	$0$	$8$	$0$		$2^{10}\cdot 13$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+(1-\beta _{6})q^{5}+\beta _{7}q^{7}+(-5+\cdots)q^{9}+\cdots$
464.3.d.b	$464$	$3$	464.d	4.b	$2$	$20$	$20$	$12.643$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		464.3.d.b	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{36}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{3}-\beta _{3}q^{5}-\beta _{12}q^{7}+(-3+\cdots)q^{9}+\cdots$
464.3.h.a	$464$	$3$	464.h	116.d	$2$	$4$	$4$	$12.643$	$\Q(\sqrt{5}, \sqrt{-6})$	$_{}$	None	None		✓			464.3.h.a	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-q^{5}-\beta _{2}q^{7}-4q^{9}-3\beta _{1}q^{11}+\cdots$

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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.