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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 54 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
1672.1.d.a	$1672$	$1$	1672.d	1672.d	$2$	$1$	$1$	$0.834$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-418}) $	$\Q(\sqrt{209}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}-q^{11}+q^{16}+\cdots$
1672.1.d.b	$1672$	$1$	1672.d	1672.d	$2$	$1$	$1$	$0.834$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-418}) $	$\Q(\sqrt{209}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}-q^{11}+q^{16}+\cdots$
1672.1.be.a	$1672$	$1$	1672.be	1672.ae	$6$	$2$	$1$	$0.834$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}-\zeta_{6}q^{9}+q^{11}+\cdots$
1672.1.be.b	$1672$	$1$	1672.be	1672.ae	$6$	$2$	$1$	$0.834$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}q^{9}-q^{11}+\cdots$
1672.1.bg.a	$1672$	$1$	1672.bg	1672.ag	$6$	$2$	$1$	$0.834$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$3$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+(-1+\cdots)q^{6}+\cdots$
1672.1.bg.b	$1672$	$1$	1672.bg	1672.ag	$6$	$2$	$1$	$0.834$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$3$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+(1+\cdots)q^{6}+\cdots$
1672.1.bu.a	$1672$	$1$	1672.bu	1672.au	$10$	$4$	$1$	$0.834$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-\zeta_{10}q^{2}+(-\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
1672.1.bu.b	$1672$	$1$	1672.bu	1672.au	$10$	$4$	$1$	$0.834$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{10}q^{2}+(\zeta_{10}^{2}-\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
1672.1.cc.a	$1672$	$1$	1672.cc	1672.bc	$18$	$6$	$1$	$0.834$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$		$1$		$q+\zeta_{18}^{7}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{8})q^{3}+\cdots$
1672.1.cc.b	$1672$	$1$	1672.cc	1672.bc	$18$	$6$	$1$	$0.834$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$		$1$		$q-\zeta_{18}^{7}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{8})q^{3}+\cdots$
1672.1.cj.a	$1672$	$1$	1672.cj	1672.bj	$18$	$6$	$1$	$0.834$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}-\zeta_{18}^{3}q^{8}+\cdots$
1672.1.cj.b	$1672$	$1$	1672.cj	1672.bj	$18$	$6$	$1$	$0.834$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}+\zeta_{18}^{3}q^{8}+\cdots$
1672.1.cn.a	$1672$	$1$	1672.cn	1672.bn	$30$	$8$	$1$	$0.834$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-3$	$0$	$0$		$1$		$q+\zeta_{30}q^{2}+(\zeta_{30}^{12}-\zeta_{30}^{14})q^{3}+\zeta_{30}^{2}q^{4}+\cdots$
1672.1.cn.b	$1672$	$1$	1672.cn	1672.bn	$30$	$8$	$1$	$0.834$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-3$	$0$	$0$		$1$		$q-\zeta_{30}q^{2}+(-\zeta_{30}^{2}-\zeta_{30}^{9})q^{3}+\zeta_{30}^{2}q^{4}+\cdots$
1672.1.cy.a	$1672$	$1$	1672.cy	1672.by	$30$	$8$	$1$	$0.834$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q-\zeta_{30}q^{2}+(\zeta_{30}^{2}-\zeta_{30}^{9})q^{3}+\zeta_{30}^{2}q^{4}+\cdots$
1672.1.cy.b	$1672$	$1$	1672.cy	1672.by	$30$	$8$	$1$	$0.834$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q-\zeta_{30}q^{2}+(\zeta_{30}^{12}+\zeta_{30}^{14})q^{3}+\zeta_{30}^{2}q^{4}+\cdots$
1672.1.di.a	$1672$	$1$	1672.di	1672.ci	$90$	$24$	$1$	$0.834$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q+\zeta_{90}^{22}q^{2}+(\zeta_{90}^{38}-\zeta_{90}^{39})q^{3}+\cdots$
1672.1.di.b	$1672$	$1$	1672.di	1672.ci	$90$	$24$	$1$	$0.834$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q+\zeta_{90}^{22}q^{2}+(-\zeta_{90}^{3}-\zeta_{90}^{29})q^{3}+\cdots$
1672.1.dn.a	$1672$	$1$	1672.dn	1672.cn	$90$	$24$	$1$	$0.834$	$\Q(\zeta_{45})$	$D_{90}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q-\zeta_{90}^{8}q^{2}+(\zeta_{90}^{6}-\zeta_{90}^{22})q^{3}+\zeta_{90}^{16}q^{4}+\cdots$
1672.1.dn.b	$1672$	$1$	1672.dn	1672.cn	$90$	$24$	$1$	$0.834$	$\Q(\zeta_{45})$	$D_{90}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q+\zeta_{90}^{8}q^{2}+(\zeta_{90}^{31}+\zeta_{90}^{42})q^{3}+\cdots$
1672.2.a.a	$1672$	$2$	1672.a	1.a	$1$	$1$	$1$	$13.351$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-3q^{9}-q^{11}+2q^{13}+\cdots$
1672.2.a.b	$1672$	$2$	1672.a	1.a	$1$	$1$	$1$	$13.351$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots$
1672.2.a.c	$1672$	$2$	1672.a	1.a	$1$	$1$	$1$	$13.351$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-3q^{7}-2q^{9}-q^{11}+\cdots$
1672.2.a.d	$1672$	$2$	1672.a	1.a	$1$	$2$	$2$	$13.351$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}+(1-\beta )q^{7}+\beta q^{9}-q^{11}+\cdots$
1672.2.a.e	$1672$	$2$	1672.a	1.a	$1$	$3$	$3$	$13.351$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}+(1+\beta _{1})q^{7}+\beta _{2}q^{9}+\cdots$
1672.2.a.f	$1672$	$2$	1672.a	1.a	$1$	$4$	$4$	$13.351$	4.4.13676.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
1672.2.a.g	$1672$	$2$	1672.a	1.a	$1$	$5$	$5$	$13.351$	5.5.3979184.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$7$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}+(1+\beta _{1})q^{5}+(2-\beta _{1})q^{7}+\cdots$
1672.2.a.h	$1672$	$2$	1672.a	1.a	$1$	$6$	$6$	$13.351$	6.6.57500224.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots$
1672.2.a.i	$1672$	$2$	1672.a	1.a	$1$	$6$	$6$	$13.351$	6.6.106392688.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{5})q^{5}-\beta _{5}q^{7}+\cdots$
1672.2.a.j	$1672$	$2$	1672.a	1.a	$1$	$6$	$6$	$13.351$	6.6.576096652.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
1672.2.a.k	$1672$	$2$	1672.a	1.a	$1$	$9$	$9$	$13.351$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$6$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{7})q^{5}+\beta _{8}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
1672.2.f.a	$1672$	$2$	1672.f	209.d	$2$	$2$	$2$	$13.351$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{5}-\beta q^{7}+3q^{9}+(-3+\beta )q^{11}+\cdots$
1672.2.f.b	$1672$	$2$	1672.f	209.d	$2$	$2$	$2$	$13.351$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{5}+\beta q^{7}+3q^{9}+(-3-\beta )q^{11}+\cdots$
1672.2.f.c	$1672$	$2$	1672.f	209.d	$2$	$28$	$28$	$13.351$		$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$
1672.2.f.d	$1672$	$2$	1672.f	209.d	$2$	$28$	$28$	$13.351$		$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$
1672.2.q.a	$1672$	$2$	1672.q	19.c	$3$	$2$	$1$	$13.351$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-1$	$-3$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}-4q^{7}+\cdots$
1672.2.q.b	$1672$	$2$	1672.q	19.c	$3$	$2$	$1$	$13.351$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
1672.2.q.c	$1672$	$2$	1672.q	19.c	$3$	$2$	$1$	$13.351$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+2q^{7}-\zeta_{6}q^{9}+q^{11}+\cdots$
1672.2.q.d	$1672$	$2$	1672.q	19.c	$3$	$4$	$2$	$13.351$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
1672.2.q.e	$1672$	$2$	1672.q	19.c	$3$	$4$	$2$	$13.351$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{3}-\beta _{1}q^{5}+(-1+\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots$
1672.2.q.f	$1672$	$2$	1672.q	19.c	$3$	$18$	$9$	$13.351$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$2$	$-12$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{8}-\beta _{14}+\beta _{15}+\cdots)q^{5}+\cdots$
1672.2.q.g	$1672$	$2$	1672.q	19.c	$3$	$18$	$9$	$13.351$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$3$	$8$	$12$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{3})q^{3}+(-\beta _{4}-\beta _{10})q^{5}+\cdots$
1672.2.q.h	$1672$	$2$	1672.q	19.c	$3$	$24$	$12$	$13.351$		$_{}$	None	None		$2$	$0$	$0$	$1$	$-4$	$12$			$\mathrm{SU}(2)[C_{3}]$
1672.2.q.i	$1672$	$2$	1672.q	19.c	$3$	$26$	$13$	$13.351$		$_{}$	None	None		$2$	$0$	$0$	$2$	$-3$	$4$			$\mathrm{SU}(2)[C_{3}]$
1672.3.i.a	$1672$	$3$	1672.i	19.b	$2$	$100$	$100$	$45.559$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-32$			$\mathrm{SU}(2)[C_{2}]$
1672.4.a.a	$1672$	$4$	1672.a	1.a	$1$	$1$	$1$	$98.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-8$	$6$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}+6q^{5}-4q^{7}+37q^{9}+11q^{11}+\cdots$
1672.4.a.b	$1672$	$4$	1672.a	1.a	$1$	$14$	$14$	$98.651$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-24$	$-3$	$-$	$2^{9}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-2-\beta _{7})q^{5}+\beta _{8}q^{7}+(7+\cdots)q^{9}+\cdots$
1672.4.a.c	$1672$	$4$	1672.a	1.a	$1$	$15$	$15$	$98.651$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$18$	$6$	$14$	$+$	$2^{10}\cdot 3$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+\beta _{4}q^{5}+(1+\beta _{8})q^{7}+\cdots$
1672.4.a.d	$1672$	$4$	1672.a	1.a	$1$	$16$	$16$	$98.651$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-14$	$-13$	$-18$	$-$	$2^{13}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots$
1672.4.a.e	$1672$	$4$	1672.a	1.a	$1$	$16$	$16$	$98.651$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$10$	$7$	$3$	$+$	$2^{12}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{8}q^{5}-\beta _{5}q^{7}+(10+\cdots)q^{9}+\cdots$

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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.