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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 56 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
3751.1.d.a	$3751$	$1$	3751.d	31.b	$2$	$1$	$1$	$1.872$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{341}) $	✓	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-q^{4}+2q^{5}+q^{9}+q^{16}-2q^{20}+\cdots$
3751.1.d.b	$3751$	$1$	3751.d	31.b	$2$	$1$	$1$	$1.872$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$1$		$1$		$q+q^{2}-q^{5}+q^{7}-q^{8}+q^{9}-q^{10}+\cdots$
3751.1.d.c	$3751$	$1$	3751.d	31.b	$2$	$2$	$2$	$1.872$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{2}+2q^{4}-q^{5}-\beta q^{7}-\beta q^{8}+\cdots$
3751.1.d.d	$3751$	$1$	3751.d	31.b	$2$	$3$	$3$	$1.872$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
3751.1.d.e	$3751$	$1$	3751.d	31.b	$2$	$3$	$3$	$1.872$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
3751.1.d.f	$3751$	$1$	3751.d	31.b	$2$	$6$	$6$	$1.872$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-31}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
3751.1.l.a	$3751$	$1$	3751.l	341.l	$6$	$4$	$2$	$1.872$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}+\beta _{2}q^{9}+q^{16}+\cdots$
3751.1.n.a	$3751$	$1$	3751.n	31.e	$6$	$2$	$1$	$1.872$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+q^{16}+\zeta_{6}^{2}q^{20}+\cdots$
3751.1.o.a	$3751$	$1$	3751.o	341.o	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$3$	$0$		$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{3}+q^{4}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
3751.1.q.a	$3751$	$1$	3751.q	341.q	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}-\zeta_{10}^{4}q^{4}+\cdots$
3751.1.r.a	$3751$	$1$	3751.r	341.r	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-5$	$3$	$0$		$1$		$q+(-1+\zeta_{10}^{4})q^{3}-\zeta_{10}^{4}q^{4}+(1-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
3751.1.s.a	$3751$	$1$	3751.s	341.s	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$5$	$-2$	$0$		$1$		$q+(1-\zeta_{10}^{2})q^{3}+\zeta_{10}q^{4}+(-\zeta_{10}+\cdots)q^{5}+\cdots$
3751.1.t.a	$3751$	$1$	3751.t	341.t	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$-1$	$0$	$1$	$-1$		$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{2}q^{5}-\zeta_{10}q^{7}-\zeta_{10}^{4}q^{8}+\cdots$
3751.1.t.b	$3751$	$1$	3751.t	341.t	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{341}) $		$16$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{10}q^{4}+\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+\zeta_{10}^{2}q^{16}+\cdots$
3751.1.t.c	$3751$	$1$	3751.t	341.t	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$1$	$0$	$1$	$1$		$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{2}q^{5}+\zeta_{10}q^{7}+\zeta_{10}^{4}q^{8}+\cdots$
3751.1.t.d	$3751$	$1$	3751.t	341.t	$10$	$8$	$2$	$1.872$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-31}) $	None		$16$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta _{7}q^{2}+2\beta _{4}q^{4}+(1+\beta _{2}+\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots$
3751.1.t.e	$3751$	$1$	3751.t	341.t	$10$	$12$	$3$	$1.872$	12.0.$\cdots$.1	$D_{9}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{5}q^{2}+(\beta _{6}+\beta _{7}-\beta _{8})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
3751.1.t.f	$3751$	$1$	3751.t	341.t	$10$	$12$	$3$	$1.872$	12.0.$\cdots$.1	$D_{9}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{5}q^{2}+(\beta _{6}+\beta _{7}-\beta _{8})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
3751.1.t.g	$3751$	$1$	3751.t	341.t	$10$	$24$	$6$	$1.872$	24.0.$\cdots$.2	$D_{18}$	$\Q(\sqrt{-31}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\beta _{1}-\beta _{9}+\beta _{11}-\beta _{14}+\beta _{17}+\cdots)q^{2}+\cdots$
3751.1.u.a	$3751$	$1$	3751.u	31.f	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(\zeta_{10}-\zeta_{10}^{3})q^{3}+\zeta_{10}q^{4}+(\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
3751.1.x.a	$3751$	$1$	3751.x	341.x	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$3$	$3$	$0$		$1$		$q+(1-\zeta_{10}^{3})q^{3}-\zeta_{10}^{3}q^{4}+(1-\zeta_{10}+\cdots)q^{5}+\cdots$
3751.1.y.a	$3751$	$1$	3751.y	341.y	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$3$	$-2$	$0$		$1$		$q+(1-\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+(-\zeta_{10}+\cdots)q^{5}+\cdots$
3751.1.be.a	$3751$	$1$	3751.be	341.ae	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q+(-\zeta_{10}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
3751.1.bf.a	$3751$	$1$	3751.bf	341.af	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q+(-\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}-q^{4}+(1-\zeta_{10}+\cdots)q^{5}+\cdots$
3751.1.br.a	$3751$	$1$	3751.br	341.an	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$-6$	$0$		$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{14})q^{3}+q^{4}+(-\zeta_{30}^{5}+\cdots)q^{5}+\cdots$
3751.1.bs.a	$3751$	$1$	3751.bs	31.h	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{11})q^{3}-\zeta_{30}^{6}q^{4}+(\zeta_{30}^{2}+\cdots)q^{5}+\cdots$
3751.1.bt.a	$3751$	$1$	3751.bt	341.ap	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{30}^{6}q^{4}+\zeta_{30}^{7}q^{5}-\zeta_{30}^{13}q^{9}+\cdots$
3751.1.bu.a	$3751$	$1$	3751.bu	341.aq	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-5$	$-1$	$0$		$1$		$q+(\zeta_{30}^{10}+\zeta_{30}^{13})q^{3}+\zeta_{30}^{9}q^{4}+\cdots$
3751.1.bv.a	$3751$	$1$	3751.bv	341.ar	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$5$	$9$	$0$		$1$		$q+(\zeta_{30}^{5}-\zeta_{30}^{11})q^{3}-\zeta_{30}^{6}q^{4}+(1+\cdots)q^{5}+\cdots$
3751.1.bw.a	$3751$	$1$	3751.bw	341.as	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(-\zeta_{30}^{2}+\zeta_{30}^{8})q^{3}+\zeta_{30}^{9}q^{4}+\cdots$
3751.1.bx.a	$3751$	$1$	3751.bx	341.at	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$-1$	$0$		$1$		$q+(-\zeta_{30}+\zeta_{30}^{4})q^{3}-\zeta_{30}^{3}q^{4}+(-\zeta_{30}+\cdots)q^{5}+\cdots$
3751.1.cd.a	$3751$	$1$	3751.cd	341.az	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-3$	$-1$	$0$		$1$		$q+(-\zeta_{30}^{5}-\zeta_{30}^{11})q^{3}-\zeta_{30}^{3}q^{4}+\cdots$
3751.1.ce.a	$3751$	$1$	3751.ce	341.ba	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-3$	$9$	$0$		$1$		$q+(\zeta_{30}^{10}-\zeta_{30}^{13})q^{3}-\zeta_{30}^{3}q^{4}+\cdots$
3751.1.cf.a	$3751$	$1$	3751.cf	341.bb	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{3}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$2$	$-1$	$0$		$1$		$q+\zeta_{30}^{2}q^{3}-\zeta_{30}^{3}q^{4}+\zeta_{30}q^{5}+3\zeta_{30}^{4}q^{9}+\cdots$
3751.1.cf.b	$3751$	$1$	3751.cf	341.bb	$30$	$16$	$2$	$1.872$	16.0.$\cdots$.1	$S_{4}$	None	None		$16$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\beta _{11}q^{4}+(1+\beta _{1}-\beta _{7}-\beta _{9}-\beta _{15})q^{5}+\cdots$
3751.1.ch.a	$3751$	$1$	3751.ch	341.bd	$30$	$8$	$1$	$1.872$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-6$	$0$		$1$		$q+(\zeta_{30}-\zeta_{30}^{7})q^{3}-q^{4}+(-\zeta_{30}^{3}+\cdots)q^{5}+\cdots$
3751.2.a.a	$3751$	$2$	3751.a	1.a	$1$	$2$	$2$	$29.952$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
3751.2.a.b	$3751$	$2$	3751.a	1.a	$1$	$2$	$2$	$29.952$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots$
3751.2.a.c	$3751$	$2$	3751.a	1.a	$1$	$3$	$3$	$29.952$	3.3.473.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}-q^{4}+(-1-\beta _{1})q^{5}+\cdots$
3751.2.a.d	$3751$	$2$	3751.a	1.a	$1$	$3$	$3$	$29.952$	3.3.473.1	$_{}$	None	None	✓	$1$	$1$	$3$	$1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}-q^{4}+(-1-\beta _{1})q^{5}+\cdots$
3751.2.a.e	$3751$	$2$	3751.a	1.a	$1$	$4$	$4$	$29.952$	$\Q(\sqrt{3}, \sqrt{7})$	$_{}$	None	None	✓	$2$	$1$	$0$	$-4$	$-6$	$0$	$+$	$3$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+(-2-\beta _{2})q^{5}-\beta _{3}q^{7}+\cdots$
3751.2.a.f	$3751$	$2$	3751.a	1.a	$1$	$4$	$4$	$29.952$	4.4.8112.1	$_{}$	None	None	✓	$2$	$1$	$0$	$-4$	$2$	$0$	$+$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(4+\beta _{3})q^{4}-\beta _{3}q^{5}+\cdots$
3751.2.a.g	$3751$	$2$	3751.a	1.a	$1$	$4$	$4$	$29.952$	4.4.2225.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{3}q^{3}+(-1-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
3751.2.a.h	$3751$	$2$	3751.a	1.a	$1$	$8$	$8$	$29.952$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$4$	$-5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1-\beta _{1})q^{3}+(2-\beta _{5})q^{4}+\cdots$
3751.2.a.i	$3751$	$2$	3751.a	1.a	$1$	$9$	$9$	$29.952$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
3751.2.a.j	$3751$	$2$	3751.a	1.a	$1$	$9$	$9$	$29.952$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-2$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
3751.2.a.k	$3751$	$2$	3751.a	1.a	$1$	$11$	$11$	$29.952$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
3751.2.a.l	$3751$	$2$	3751.a	1.a	$1$	$15$	$15$	$29.952$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$8$	$0$	$-$	$23$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
3751.2.a.m	$3751$	$2$	3751.a	1.a	$1$	$15$	$15$	$29.952$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$8$	$0$	$-$	$23$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
3751.2.a.n	$3751$	$2$	3751.a	1.a	$1$	$16$	$16$	$29.952$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{14}q^{3}+(2+\beta _{6}+\beta _{12}+\cdots)q^{4}+\cdots$

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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.