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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 316 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
975.1.e.a	$975$	$1$	975.e	195.e	$2$	$2$	$2$	$0.487$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}+q^{4}-q^{9}-iq^{12}-iq^{13}+\cdots$
975.1.g.a	$975$	$1$	975.g	39.d	$2$	$1$	$1$	$0.487$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
975.1.g.b	$975$	$1$	975.g	39.d	$2$	$2$	$2$	$0.487$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}-\beta q^{11}+\cdots$
975.1.g.c	$975$	$1$	975.g	39.d	$2$	$2$	$2$	$0.487$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}+\beta q^{11}+\cdots$
975.1.j.a	$975$	$1$	975.j	195.j	$4$	$4$	$2$	$0.487$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
975.1.u.a	$975$	$1$	975.u	195.u	$4$	$4$	$2$	$0.487$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}-q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
975.1.x.a	$975$	$1$	975.x	39.h	$6$	$2$	$1$	$0.487$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-3$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+(-1-\zeta_{6})q^{7}+\cdots$
975.1.x.b	$975$	$1$	975.x	39.h	$6$	$2$	$1$	$0.487$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$3$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
975.1.y.a	$975$	$1$	975.y	195.x	$6$	$4$	$2$	$0.487$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots$
975.1.z.a	$975$	$1$	975.z	195.y	$6$	$4$	$2$	$0.487$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{7}+\cdots$
975.1.ba.a	$975$	$1$	975.ba	39.i	$6$	$2$	$1$	$0.487$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
975.1.ba.b	$975$	$1$	975.ba	39.i	$6$	$2$	$1$	$0.487$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
975.1.bd.a	$975$	$1$	975.bd	975.ad	$10$	$4$	$1$	$0.487$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-3$	$-1$	$1$	$0$		$1$		$q+(-1+\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
975.1.bd.b	$975$	$1$	975.bd	975.ad	$10$	$4$	$1$	$0.487$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$3$	$-1$	$-1$	$0$		$1$		$q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
975.1.bd.c	$975$	$1$	975.bd	975.ad	$10$	$8$	$2$	$0.487$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}+\zeta_{20}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots$
975.1.bi.a	$975$	$1$	975.bi	975.ai	$10$	$16$	$4$	$0.487$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{40}^{9}-\zeta_{40}^{15})q^{2}-\zeta_{40}^{14}q^{3}+\cdots$
975.1.bk.a	$975$	$1$	975.bk	195.ac	$12$	$8$	$2$	$0.487$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{4}q^{4}+(\zeta_{24}^{9}-\zeta_{24}^{11}+\cdots)q^{7}+\cdots$
975.1.bv.a	$975$	$1$	975.bv	195.an	$12$	$8$	$2$	$0.487$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{3}-\zeta_{24}^{4}q^{4}+(\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots$
975.1.cj.a	$975$	$1$	975.cj	975.bj	$30$	$16$	$2$	$0.487$	$\Q(\zeta_{60})$	$A_{5}$	None	None		$8$	$0$	$0$	$0$	$0$	$-8$		$1$		$q+(-\zeta_{60}^{11}+\zeta_{60}^{17})q^{2}+\zeta_{60}^{23}q^{3}+\cdots$
975.2.a.a	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots$
975.2.a.b	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots$
975.2.a.c	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots$
975.2.a.d	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{7}+3q^{8}+\cdots$
975.2.a.e	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots$
975.2.a.f	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots$
975.2.a.g	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{7}+q^{9}-q^{11}+2q^{12}+\cdots$
975.2.a.h	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{7}+q^{9}-q^{11}-2q^{12}+\cdots$
975.2.a.i	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
975.2.a.j	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots$
975.2.a.k	$975$	$2$	975.a	1.a	$1$	$1$	$1$	$7.785$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{7}-3q^{8}+\cdots$
975.2.a.l	$975$	$2$	975.a	1.a	$1$	$2$	$2$	$7.785$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
975.2.a.m	$975$	$2$	975.a	1.a	$1$	$3$	$3$	$7.785$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
975.2.a.n	$975$	$2$	975.a	1.a	$1$	$3$	$3$	$7.785$	3.3.564.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
975.2.a.o	$975$	$2$	975.a	1.a	$1$	$3$	$3$	$7.785$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$-1$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(3+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
975.2.a.p	$975$	$2$	975.a	1.a	$1$	$3$	$3$	$7.785$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
975.2.a.q	$975$	$2$	975.a	1.a	$1$	$3$	$3$	$7.785$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$3$	$3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
975.2.a.r	$975$	$2$	975.a	1.a	$1$	$5$	$5$	$7.785$	5.5.1821184.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-5$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
975.2.a.s	$975$	$2$	975.a	1.a	$1$	$5$	$5$	$7.785$	5.5.1821184.1	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
975.2.b.a	$975$	$2$	975.b	13.b	$2$	$2$	$2$	$7.785$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-q^{3}-2q^{4}-2iq^{6}-3iq^{7}+\cdots$
975.2.b.b	$975$	$2$	975.b	13.b	$2$	$2$	$2$	$7.785$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{3}+q^{4}-iq^{6}-2iq^{7}+\cdots$
975.2.b.c	$975$	$2$	975.b	13.b	$2$	$2$	$2$	$7.785$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+q^{3}-2q^{4}+2iq^{6}-3iq^{7}+\cdots$
975.2.b.d	$975$	$2$	975.b	13.b	$2$	$2$	$2$	$7.785$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}+q^{3}-q^{4}-\zeta_{6}q^{6}+2\zeta_{6}q^{7}+\cdots$
975.2.b.e	$975$	$2$	975.b	13.b	$2$	$2$	$2$	$7.785$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+2q^{4}-iq^{7}+q^{9}-iq^{11}+\cdots$
975.2.b.f	$975$	$2$	975.b	13.b	$2$	$4$	$4$	$7.785$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+(-3+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots$
975.2.b.g	$975$	$2$	975.b	13.b	$2$	$4$	$4$	$7.785$	4.0.27648.1	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
975.2.b.h	$975$	$2$	975.b	13.b	$2$	$4$	$4$	$7.785$	4.0.27648.1	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
975.2.b.i	$975$	$2$	975.b	13.b	$2$	$6$	$6$	$7.785$	6.0.559227904.1	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
975.2.b.j	$975$	$2$	975.b	13.b	$2$	$6$	$6$	$7.785$	6.0.50922496.1	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{3}+(-1-\beta _{5})q^{4}-\beta _{2}q^{6}+\cdots$
975.2.b.k	$975$	$2$	975.b	13.b	$2$	$6$	$6$	$7.785$	6.0.559227904.1	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
975.2.b.l	$975$	$2$	975.b	13.b	$2$	$6$	$6$	$7.785$	6.0.50922496.1	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+q^{3}+(-1-\beta _{5})q^{4}+\beta _{2}q^{6}+\cdots$

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