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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 51 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
2107.1.b.a	$2107$	$1$	2107.b	43.b	$2$	$1$	$1$	$1.052$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-43}) $	$\Q(\sqrt{301}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}-2q^{11}+q^{16}+2q^{23}+\cdots$
2107.1.b.b	$2107$	$1$	2107.b	43.b	$2$	$2$	$2$	$1.052$	$\Q(\sqrt{-1}) $	$A_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-iq^{3}-iq^{5}-q^{6}-iq^{8}+\cdots$
2107.1.b.c	$2107$	$1$	2107.b	43.b	$2$	$2$	$2$	$1.052$	$\Q(\sqrt{-1}) $	$A_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-iq^{3}-iq^{5}+q^{6}+iq^{8}+\cdots$
2107.1.b.d	$2107$	$1$	2107.b	43.b	$2$	$2$	$2$	$1.052$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-43}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}-\beta q^{13}+q^{16}+\beta q^{17}+\cdots$
2107.1.j.a	$2107$	$1$	2107.j	43.d	$6$	$2$	$1$	$1.052$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
2107.1.k.a	$2107$	$1$	2107.k	301.k	$6$	$2$	$1$	$1.052$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{2}+q^{8}+q^{9}+\zeta_{6}^{2}q^{11}+\zeta_{6}q^{16}+\cdots$
2107.1.l.a	$2107$	$1$	2107.l	301.l	$6$	$2$	$1$	$1.052$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+q^{8}-\zeta_{6}q^{9}-\zeta_{6}q^{11}+\cdots$
2107.1.n.a	$2107$	$1$	2107.n	301.n	$6$	$2$	$1$	$1.052$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q+(-1+\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots$
2107.1.q.a	$2107$	$1$	2107.q	301.q	$6$	$2$	$1$	$1.052$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q+(1+\zeta_{6})q^{2}+(1+\zeta_{6}+\zeta_{6}^{2})q^{4}+(\zeta_{6}+\cdots)q^{8}+\cdots$
2107.1.r.a	$2107$	$1$	2107.r	301.r	$6$	$2$	$1$	$1.052$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-43}) $	$\Q(\sqrt{301}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}q^{16}+\cdots$
2107.1.r.b	$2107$	$1$	2107.r	301.r	$6$	$4$	$2$	$1.052$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-43}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-1-\beta _{2})q^{4}+\beta _{2}q^{9}-\beta _{3}q^{13}+\cdots$
2107.1.r.c	$2107$	$1$	2107.r	301.r	$6$	$4$	$2$	$1.052$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{5}+q^{6}+\cdots$
2107.1.bx.a	$2107$	$1$	2107.bx	43.f	$14$	$6$	$1$	$1.052$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{14}^{2}+\zeta_{14}^{3})q^{2}+(\zeta_{14}^{4}+\zeta_{14}^{5}+\cdots)q^{4}+\cdots$
2107.1.eg.a	$2107$	$1$	2107.eg	301.ae	$42$	$12$	$1$	$1.052$	$\Q(\zeta_{21})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{42}^{10}+\zeta_{42}^{16})q^{2}+(\zeta_{42}^{5}-\zeta_{42}^{11}+\cdots)q^{4}+\cdots$
2107.1.eh.a	$2107$	$1$	2107.eh	301.af	$42$	$12$	$1$	$1.052$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q+(\zeta_{42}^{18}-\zeta_{42}^{20})q^{2}+(-\zeta_{42}^{15}+\cdots)q^{4}+\cdots$
2107.1.ez.a	$2107$	$1$	2107.ez	301.ai	$42$	$12$	$1$	$1.052$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q+(-\zeta_{42}^{18}-\zeta_{42}^{19})q^{2}+(-\zeta_{42}^{15}+\cdots)q^{4}+\cdots$
2107.1.fj.a	$2107$	$1$	2107.fj	301.aj	$42$	$12$	$1$	$1.052$	$\Q(\zeta_{21})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(-\zeta_{42}^{5}+\zeta_{42}^{8})q^{2}+(\zeta_{42}^{10}-\zeta_{42}^{13}+\cdots)q^{4}+\cdots$
2107.1.fu.a	$2107$	$1$	2107.fu	301.ak	$42$	$12$	$1$	$1.052$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+(-\zeta_{42}-\zeta_{42}^{3})q^{2}+(\zeta_{42}^{2}+\zeta_{42}^{4}+\cdots)q^{4}+\cdots$
2107.1.ga.a	$2107$	$1$	2107.ga	301.al	$42$	$12$	$1$	$1.052$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+(\zeta_{42}^{6}-\zeta_{42}^{11})q^{2}+(-\zeta_{42}+\zeta_{42}^{12}+\cdots)q^{4}+\cdots$
2107.1.ge.a	$2107$	$1$	2107.ge	43.h	$42$	$12$	$1$	$1.052$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{42}^{11}+\zeta_{42}^{13})q^{2}+(-\zeta_{42}+\cdots)q^{4}+\cdots$
2107.2.a.a	$2107$	$2$	2107.a	1.a	$1$	$1$	$1$	$16.824$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}+4q^{5}-4q^{6}+\cdots$
2107.2.a.b	$2107$	$2$	2107.a	1.a	$1$	$2$	$2$	$16.824$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}+(-2+\beta )q^{5}+2q^{6}+\cdots$
2107.2.a.c	$2107$	$2$	2107.a	1.a	$1$	$2$	$2$	$16.824$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$3$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(1-2\beta )q^{5}+\cdots$
2107.2.a.d	$2107$	$2$	2107.a	1.a	$1$	$2$	$2$	$16.824$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots$
2107.2.a.e	$2107$	$2$	2107.a	1.a	$1$	$4$	$4$	$16.824$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$3$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2107.2.a.f	$2107$	$2$	2107.a	1.a	$1$	$5$	$5$	$16.824$	5.5.81509.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(1+\beta _{3}+\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
2107.2.a.g	$2107$	$2$	2107.a	1.a	$1$	$5$	$5$	$16.824$	5.5.301909.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-5$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2107.2.a.h	$2107$	$2$	2107.a	1.a	$1$	$7$	$7$	$16.824$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$-1$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}+(2-\beta _{2}+\beta _{6})q^{4}+\cdots$
2107.2.a.i	$2107$	$2$	2107.a	1.a	$1$	$8$	$8$	$16.824$	8.8.$\cdots$.1	$_{}$	None	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}-\beta _{6}q^{3}+(1+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
2107.2.a.j	$2107$	$2$	2107.a	1.a	$1$	$12$	$12$	$16.824$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-4$	$-14$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{2}-\beta _{10})q^{3}+(1-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
2107.2.a.k	$2107$	$2$	2107.a	1.a	$1$	$12$	$12$	$16.824$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-3$	$4$	$14$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{10})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
2107.2.a.l	$2107$	$2$	2107.a	1.a	$1$	$12$	$12$	$16.824$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1+\beta _{11})q^{2}-\beta _{1}q^{3}+(2-\beta _{9}+\beta _{11})q^{4}+\cdots$
2107.2.a.m	$2107$	$2$	2107.a	1.a	$1$	$14$	$14$	$16.824$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$-14$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{13}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
2107.2.a.n	$2107$	$2$	2107.a	1.a	$1$	$14$	$14$	$16.824$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$14$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{13}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
2107.2.a.o	$2107$	$2$	2107.a	1.a	$1$	$18$	$18$	$16.824$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	$2$	$1$	$-10$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{5})q^{2}+\beta _{1}q^{3}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
2107.2.a.p	$2107$	$2$	2107.a	1.a	$1$	$26$	$26$	$16.824$		$_{}$	None	None	✓	$2$	$0$	$10$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$
2107.4.a.a	$2107$	$4$	2107.a	1.a	$1$	$1$	$1$	$124.317$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$3$	$-10$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-10q^{3}+q^{4}-6q^{5}-30q^{6}+\cdots$
2107.4.a.b	$2107$	$4$	2107.a	1.a	$1$	$4$	$4$	$124.317$	4.4.45868.1	$_{}$	None	None	✓	$1$	$0$	$-4$	$11$	$27$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(3-\beta _{2}+\beta _{3})q^{3}+\cdots$
2107.4.a.c	$2107$	$4$	2107.a	1.a	$1$	$6$	$6$	$124.317$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$6$	$-7$	$-43$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
2107.4.a.d	$2107$	$4$	2107.a	1.a	$1$	$14$	$14$	$124.317$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-10$	$11$	$23$	$0$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{6})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
2107.4.a.e	$2107$	$4$	2107.a	1.a	$1$	$16$	$16$	$124.317$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-4$	$9$	$43$	$0$	$+$	$2\cdot 7$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(4+\beta _{2})q^{4}+\cdots$
2107.4.a.f	$2107$	$4$	2107.a	1.a	$1$	$16$	$16$	$124.317$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-15$	$-7$	$0$	$-$	$2^{2}\cdot 3^{3}\cdot 13$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{7})q^{3}+(5+\beta _{2})q^{4}+\cdots$
2107.4.a.g	$2107$	$4$	2107.a	1.a	$1$	$17$	$17$	$124.317$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$9$	$-3$	$-21$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{7}q^{3}+(6-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2107.4.a.h	$2107$	$4$	2107.a	1.a	$1$	$30$	$30$	$124.317$		$_{}$	None	None	✓	$2$	$1$	$-8$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$
2107.4.a.i	$2107$	$4$	2107.a	1.a	$1$	$34$	$34$	$124.317$		$_{}$	None	None	✓	$2$	$0$	$12$	$0$	$0$	$0$	$+$		$\mathrm{SU}(2)$
2107.4.a.j	$2107$	$4$	2107.a	1.a	$1$	$42$	$42$	$124.317$		$_{}$	None	None	✓	$1$	$1$	$0$	$-18$	$-70$	$0$	$-$		$\mathrm{SU}(2)$
2107.4.a.k	$2107$	$4$	2107.a	1.a	$1$	$42$	$42$	$124.317$		$_{}$	None	None	✓	$1$	$1$	$0$	$-18$	$-70$	$0$	$-$		$\mathrm{SU}(2)$
2107.4.a.l	$2107$	$4$	2107.a	1.a	$1$	$42$	$42$	$124.317$		$_{}$	None	None	✓	$1$	$0$	$0$	$18$	$70$	$0$	$+$		$\mathrm{SU}(2)$
2107.4.a.m	$2107$	$4$	2107.a	1.a	$1$	$42$	$42$	$124.317$		$_{}$	None	None	✓	$1$	$0$	$0$	$18$	$70$	$0$	$+$		$\mathrm{SU}(2)$
2107.4.a.n	$2107$	$4$	2107.a	1.a	$1$	$58$	$58$	$124.317$		$_{}$	None	None	✓	$2$	$1$	$-20$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$

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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.