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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 136 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
3200.1.e.a	$3200$	$1$	3200.e	40.e	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+q^{9}-iq^{17}+q^{41}-q^{49}+iq^{73}+\cdots$
3200.1.e.b	$3200$	$1$	3200.e	40.e	$2$	$4$	$4$	$1.597$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
3200.1.g.a	$3200$	$1$	3200.g	8.d	$2$	$1$	$1$	$1.597$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{9}+2q^{17}+2q^{41}+q^{49}+2q^{73}+\cdots$
3200.1.g.b	$3200$	$1$	3200.g	8.d	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-q^{9}-iq^{13}-iq^{37}-q^{41}+q^{49}+\cdots$
3200.1.g.c	$3200$	$1$	3200.g	8.d	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}+2q^{9}-\beta q^{11}-q^{17}+\beta q^{19}+\cdots$
3200.1.g.d	$3200$	$1$	3200.g	8.d	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta q^{3}+2q^{9}-\beta q^{11}+q^{17}+\beta q^{19}+\cdots$
3200.1.g.e	$3200$	$1$	3200.g	8.d	$2$	$4$	$4$	$1.597$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots$
3200.1.m.a	$3200$	$1$	3200.m	40.i	$4$	$2$	$1$	$1.597$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{9}+(-1-i)q^{13}+(-1-i)q^{17}+\cdots$
3200.1.m.b	$3200$	$1$	3200.m	40.i	$4$	$2$	$1$	$1.597$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{9}+(1+i)q^{13}+(-1-i)q^{17}+\cdots$
3200.1.m.c	$3200$	$1$	3200.m	40.i	$4$	$4$	$2$	$1.597$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{2}) $		$16$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\zeta_{8}q^{23}-q^{41}+\cdots$
3200.1.m.d	$3200$	$1$	3200.m	40.i	$4$	$4$	$2$	$1.597$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{10}) $		$16$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q-\zeta_{8}^{3}q^{3}-3\zeta_{8}^{2}q^{9}+2\zeta_{8}q^{27}+q^{41}+\cdots$
3200.1.m.e	$3200$	$1$	3200.m	40.i	$4$	$8$	$4$	$1.597$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{4}-\zeta_{24}^{8})q^{11}+\cdots$
3200.1.bd.a	$3200$	$1$	3200.bd	200.n	$10$	$4$	$1$	$1.597$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{9}+(-\zeta_{10}+\zeta_{10}^{3}+\cdots)q^{13}+\cdots$
3200.1.bd.b	$3200$	$1$	3200.bd	200.n	$10$	$4$	$1$	$1.597$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{9}+(\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{13}+\cdots$
3200.1.bi.a	$3200$	$1$	3200.bi	200.s	$10$	$4$	$1$	$1.597$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{13}+\cdots$
3200.1.bi.b	$3200$	$1$	3200.bi	200.s	$10$	$4$	$1$	$1.597$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots$
3200.1.bz.a	$3200$	$1$	3200.bz	200.x	$20$	$8$	$1$	$1.597$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(\zeta_{20}^{3}-\zeta_{20}^{6}+\cdots)q^{13}+\cdots$
3200.1.bz.b	$3200$	$1$	3200.bz	200.x	$20$	$8$	$1$	$1.597$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(-\zeta_{20}^{3}+\zeta_{20}^{6}+\cdots)q^{13}+\cdots$
3200.2.a.a	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$0$	$-3$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-4q^{7}+6q^{9}-3q^{11}-2q^{13}+\cdots$
3200.2.a.b	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-4q^{7}+6q^{9}+3q^{11}+2q^{13}+\cdots$
3200.2.a.c	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+4q^{7}+6q^{9}-3q^{11}+2q^{13}+\cdots$
3200.2.a.d	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+4q^{7}+6q^{9}+3q^{11}-2q^{13}+\cdots$
3200.2.a.e	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
3200.2.a.f	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+2q^{11}-2q^{13}-6q^{17}+\cdots$
3200.2.a.g	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+2q^{11}+2q^{13}-6q^{17}+\cdots$
3200.2.a.h	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
3200.2.a.i	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-q^{11}-2q^{13}-3q^{17}+\cdots$
3200.2.a.j	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-q^{11}+2q^{13}-3q^{17}+\cdots$
3200.2.a.k	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+q^{11}-2q^{13}+3q^{17}+\cdots$
3200.2.a.l	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+q^{11}+2q^{13}+3q^{17}+\cdots$
3200.2.a.m	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}-6q^{11}+2q^{13}+6q^{17}+\cdots$
3200.2.a.n	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}+6q^{11}-2q^{13}+6q^{17}+\cdots$
3200.2.a.o	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-6q^{11}-2q^{13}+6q^{17}+\cdots$
3200.2.a.p	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}+6q^{11}+2q^{13}+6q^{17}+\cdots$
3200.2.a.q	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}-q^{11}-2q^{13}+3q^{17}+\cdots$
3200.2.a.r	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}-q^{11}+2q^{13}+3q^{17}+\cdots$
3200.2.a.s	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+q^{11}-2q^{13}-3q^{17}+\cdots$
3200.2.a.t	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+q^{11}+2q^{13}-3q^{17}+\cdots$
3200.2.a.u	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
3200.2.a.v	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-2q^{11}-2q^{13}-6q^{17}+\cdots$
3200.2.a.w	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-2q^{11}+2q^{13}-6q^{17}+\cdots$
3200.2.a.x	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
3200.2.a.y	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{7}+6q^{9}-3q^{11}-2q^{13}+\cdots$
3200.2.a.z	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{7}+6q^{9}+3q^{11}+2q^{13}+\cdots$
3200.2.a.ba	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+4q^{7}+6q^{9}-3q^{11}+2q^{13}+\cdots$
3200.2.a.bb	$3200$	$2$	3200.a	1.a	$1$	$1$	$1$	$25.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+4q^{7}+6q^{9}+3q^{11}-2q^{13}+\cdots$
3200.2.a.bc	$3200$	$2$	3200.a	1.a	$1$	$2$	$2$	$25.552$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-2-2\beta )q^{7}-2\beta q^{9}+\cdots$
3200.2.a.bd	$3200$	$2$	3200.a	1.a	$1$	$2$	$2$	$25.552$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-2-2\beta )q^{7}-2\beta q^{9}+\cdots$
3200.2.a.be	$3200$	$2$	3200.a	1.a	$1$	$2$	$2$	$25.552$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
3200.2.a.bf	$3200$	$2$	3200.a	1.a	$1$	$2$	$2$	$25.552$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(1-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$

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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.