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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 59 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
2535.1.e.a	$2535$	$1$	2535.e	195.e	$2$	$6$	$6$	$1.265$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$-6$	$0$	$0$		$1$		$q+(-\beta _{1}+\beta _{3}+\beta _{5})q^{2}-q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
2535.1.e.b	$2535$	$1$	2535.e	195.e	$2$	$6$	$6$	$1.265$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$6$	$0$	$0$		$1$		$q+(-\beta _{1}+\beta _{3}+\beta _{5})q^{2}+q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
2535.1.f.a	$2535$	$1$	2535.f	15.d	$2$	$3$	$3$	$1.265$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$-3$	$3$	$0$		$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
2535.1.f.b	$2535$	$1$	2535.f	15.d	$2$	$3$	$3$	$1.265$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$3$	$3$	$0$		$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2535.1.f.c	$2535$	$1$	2535.f	15.d	$2$	$3$	$3$	$1.265$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$-3$	$-3$	$0$		$1$		$q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots$
2535.1.f.d	$2535$	$1$	2535.f	15.d	$2$	$3$	$3$	$1.265$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$3$	$-3$	$0$		$1$		$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
2535.1.f.e	$2535$	$1$	2535.f	15.d	$2$	$4$	$4$	$1.265$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}+q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
2535.1.j.a	$2535$	$1$	2535.j	195.j	$4$	$8$	$4$	$1.265$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}-\zeta_{16}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots$
2535.1.u.a	$2535$	$1$	2535.u	195.u	$4$	$8$	$4$	$1.265$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}^{3}+\zeta_{16}^{5})q^{2}-\zeta_{16}^{6}q^{3}+\cdots$
2535.1.x.a	$2535$	$1$	2535.x	195.x	$6$	$6$	$3$	$1.265$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$-3$	$-6$	$0$		$1$		$q+(\beta _{3}+\beta _{4})q^{2}-\beta _{5}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
2535.1.x.b	$2535$	$1$	2535.x	195.x	$6$	$6$	$3$	$1.265$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$3$	$-6$	$0$		$1$		$q+(\beta _{1}-\beta _{2})q^{2}+\beta _{5}q^{3}+(-\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots$
2535.1.x.c	$2535$	$1$	2535.x	195.x	$6$	$6$	$3$	$1.265$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$-3$	$6$	$0$		$1$		$q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+\cdots$
2535.1.x.d	$2535$	$1$	2535.x	195.x	$6$	$6$	$3$	$1.265$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$3$	$6$	$0$		$1$		$q+(-\beta _{3}-\beta _{4})q^{2}+\beta _{5}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
2535.1.x.e	$2535$	$1$	2535.x	195.x	$6$	$8$	$4$	$1.265$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{2}+\zeta_{24}^{2}q^{3}-\zeta_{24}^{4}q^{4}+\cdots$
2535.1.y.a	$2535$	$1$	2535.y	195.y	$6$	$8$	$4$	$1.265$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}-\zeta_{24}^{7})q^{2}+\zeta_{24}^{10}q^{3}-\zeta_{24}^{8}q^{4}+\cdots$
2535.1.y.b	$2535$	$1$	2535.y	195.y	$6$	$12$	$6$	$1.265$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$-6$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(-1+\beta _{7})q^{3}+(1-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
2535.1.y.c	$2535$	$1$	2535.y	195.y	$6$	$12$	$6$	$1.265$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$6$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(1-\beta _{7})q^{3}+(1-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
2535.1.bc.a	$2535$	$1$	2535.bc	195.ac	$12$	$16$	$4$	$1.265$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}^{5}-\zeta_{48}^{11})q^{2}+\zeta_{48}^{2}q^{3}+\cdots$
2535.1.bn.a	$2535$	$1$	2535.bn	195.an	$12$	$16$	$4$	$1.265$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}^{17}-\zeta_{48}^{23})q^{2}+\zeta_{48}^{2}q^{3}+\cdots$
2535.2.a.a	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-3q^{7}+\cdots$
2535.2.a.b	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$1$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+3q^{7}+\cdots$
2535.2.a.c	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-5q^{7}+\cdots$
2535.2.a.d	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
2535.2.a.e	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
2535.2.a.f	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots$
2535.2.a.g	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots$
2535.2.a.h	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+6q^{11}+\cdots$
2535.2.a.i	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+q^{7}+q^{9}-6q^{11}+\cdots$
2535.2.a.j	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots$
2535.2.a.k	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots$
2535.2.a.l	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+2q^{7}+\cdots$
2535.2.a.m	$2535$	$2$	2535.a	1.a	$1$	$1$	$1$	$20.242$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+5q^{7}+\cdots$
2535.2.a.n	$2535$	$2$	2535.a	1.a	$1$	$2$	$2$	$20.242$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}-q^{5}+\cdots$
2535.2.a.o	$2535$	$2$	2535.a	1.a	$1$	$2$	$2$	$20.242$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}+q^{5}+\cdots$
2535.2.a.p	$2535$	$2$	2535.a	1.a	$1$	$2$	$2$	$20.242$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
2535.2.a.q	$2535$	$2$	2535.a	1.a	$1$	$2$	$2$	$20.242$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
2535.2.a.r	$2535$	$2$	2535.a	1.a	$1$	$2$	$2$	$20.242$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots$
2535.2.a.s	$2535$	$2$	2535.a	1.a	$1$	$2$	$2$	$20.242$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+q^{5}+\cdots$
2535.2.a.t	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$-3$	$3$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
2535.2.a.u	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$-2$	$3$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
2535.2.a.v	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
2535.2.a.w	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-1$	$3$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
2535.2.a.x	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$3$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2535.2.a.y	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots$
2535.2.a.z	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+\cdots$
2535.2.a.ba	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	3.3.756.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
2535.2.a.bb	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	3.3.756.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2535.2.a.bc	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$3$	$-1$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2535.2.a.bd	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
2535.2.a.be	$2535$	$2$	2535.a	1.a	$1$	$3$	$3$	$20.242$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$-3$	$-12$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$

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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.