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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 105 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3328.1.c.a	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-26}) $	None					104.1.h.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-i q^{3}-i q^{5}-q^{7}-i q^{13}-q^{15}+\cdots$
3328.1.c.b	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-13}) $	None	✓				1664.1.h.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta q^{7}+q^{9}-\beta q^{11}-q^{13}+\beta q^{19}+\cdots$
3328.1.c.c	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-26}) $	$\Q(\sqrt{26}) $					1664.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-2 i q^{5}+q^{9}-i q^{13}+2 q^{17}-3 q^{25}+\cdots$
3328.1.c.d	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-13}) $	None	✓				1664.1.h.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\beta q^{19}+\cdots$
3328.1.c.e	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-26}) $	None					104.1.h.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+i q^{3}-i q^{5}+q^{7}-i q^{13}+q^{15}+\cdots$
3328.1.c.f	$3328$	$1$	3328.c	52.b	$2$	$4$	$4$	$1.661$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-26}) $	None			✓		1664.1.h.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{3}q^{5}+\cdots$
3328.1.h.a	$3328$	$1$	3328.h	104.h	$2$	$2$	$2$	$1.661$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $			✓	✓	208.1.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{9}-i q^{13}-2 q^{17}-q^{25}-2 i q^{29}+\cdots$
3328.1.j.a	$3328$	$1$	3328.j	104.j	$4$	$2$	$1$	$1.661$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					416.1.t.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-i-1)q^{5}+q^{9}+q^{13}+2 i q^{17}+\cdots$
3328.1.j.b	$3328$	$1$	3328.j	104.j	$4$	$2$	$1$	$1.661$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					416.1.t.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(i+1)q^{5}+q^{9}-q^{13}+2 i q^{17}+\cdots$
3328.1.m.a	$3328$	$1$	3328.m	208.m	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3328.1.m.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}-q^{13}+\cdots$
3328.1.m.b	$3328$	$1$	3328.m	208.m	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3328.1.m.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}+q^{13}+\cdots$
3328.1.o.a	$3328$	$1$	3328.o	208.o	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3328.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+(-1+\cdots)q^{11}+\cdots$
3328.1.o.b	$3328$	$1$	3328.o	208.o	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3328.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{7}+(-1+\cdots)q^{11}+\cdots$
3328.1.o.c	$3328$	$1$	3328.o	208.o	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3328.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+(1+\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
3328.1.o.d	$3328$	$1$	3328.o	208.o	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3328.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{7}+(1+\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
3328.1.r.a	$3328$	$1$	3328.r	208.r	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3328.1.m.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}-q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{13}+\cdots$
3328.1.r.b	$3328$	$1$	3328.r	208.r	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3328.1.m.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}+q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{13}+\cdots$
3328.1.t.a	$3328$	$1$	3328.t	13.d	$4$	$2$	$1$	$1.661$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					1664.1.j.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(i-1)q^{5}-q^{9}-q^{13}-2 i q^{17}+\cdots$
3328.1.t.b	$3328$	$1$	3328.t	13.d	$4$	$2$	$1$	$1.661$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					1664.1.j.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-i+1)q^{5}-q^{9}+q^{13}-2 i q^{17}+\cdots$
3328.1.t.c	$3328$	$1$	3328.t	13.d	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None					1664.1.j.c	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-q^{3}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+(1-\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
3328.1.t.d	$3328$	$1$	3328.t	13.d	$4$	$4$	$2$	$1.661$	$\Q(\zeta_{8})$	$S_{4}$	None	None					1664.1.j.c	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+q^{3}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}+(-1+\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
3328.1.v.a	$3328$	$1$	3328.v	104.n	$6$	$4$	$2$	$1.661$	$\Q(\zeta_{12})$	$A_{4}$	None	None					416.1.bb.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{11}+\cdots$
3328.1.v.b	$3328$	$1$	3328.v	104.n	$6$	$4$	$2$	$1.661$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-1}) $	None					52.1.j.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{5}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{5}q^{13}+\cdots$
3328.1.v.c	$3328$	$1$	3328.v	104.n	$6$	$4$	$2$	$1.661$	$\Q(\zeta_{12})$	$A_{4}$	None	None					416.1.bb.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{11}+\cdots$
3328.1.x.a	$3328$	$1$	3328.x	104.p	$6$	$4$	$2$	$1.661$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None			✓	✓	208.1.y.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{13}+\cdots$
3328.1.y.a	$3328$	$1$	3328.y	52.i	$6$	$4$	$2$	$1.661$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None			✓	✓	1664.1.x.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots$
3328.1.bb.a	$3328$	$1$	3328.bb	52.j	$6$	$4$	$2$	$1.661$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None					1664.1.v.c	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+(\beta _{1}-\beta _{3})q^{3}-q^{5}+(1-\beta _{2})q^{9}+\beta _{2}q^{13}+\cdots$
3328.1.bb.b	$3328$	$1$	3328.bb	52.j	$6$	$4$	$2$	$1.661$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None					1664.1.v.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots$
3328.1.bb.c	$3328$	$1$	3328.bb	52.j	$6$	$4$	$2$	$1.661$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None					1664.1.v.c	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q+(\beta _{1}-\beta _{3})q^{3}+q^{5}+(1-\beta _{2})q^{9}-\beta _{2}q^{13}+\cdots$
3328.1.bl.a	$3328$	$1$	3328.bl	13.f	$12$	$4$	$1$	$1.661$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None					1664.1.bv.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{2})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots$
3328.1.bl.b	$3328$	$1$	3328.bl	13.f	$12$	$4$	$1$	$1.661$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None					1664.1.bv.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(\zeta_{12}+\zeta_{12}^{2})q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{4}q^{13}+\cdots$
3328.1.bv.a	$3328$	$1$	3328.bv	104.x	$12$	$4$	$1$	$1.661$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None					416.1.bl.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{2})q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}^{4}q^{13}+\cdots$
3328.1.bv.b	$3328$	$1$	3328.bv	104.x	$12$	$4$	$1$	$1.661$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None					416.1.bl.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots$
3328.2.a.a	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				1664.2.b.a	$1$	$2$	$0$	$-3$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-3q^{7}+6q^{9}-6q^{11}+\cdots$
3328.2.a.b	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				1664.2.b.a	$1$	$0$	$0$	$-3$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+3q^{7}+6q^{9}-6q^{11}+\cdots$
3328.2.a.c	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				104.2.b.a	$1$	$2$	$0$	$-1$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-3q^{7}-2q^{9}+q^{13}+\cdots$
3328.2.a.d	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				1664.2.b.b	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots$
3328.2.a.e	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				1664.2.b.b	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots$
3328.2.a.f	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				104.2.b.a	$1$	$0$	$0$	$-1$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+3q^{7}-2q^{9}-q^{13}+\cdots$
3328.2.a.g	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				104.2.b.a	$1$	$1$	$0$	$1$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+3q^{7}-2q^{9}+q^{13}+\cdots$
3328.2.a.h	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				1664.2.b.b	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots$
3328.2.a.i	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				1664.2.b.b	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots$
3328.2.a.j	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				104.2.b.a	$1$	$1$	$0$	$1$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-3q^{7}-2q^{9}-q^{13}+\cdots$
3328.2.a.k	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				1664.2.b.a	$1$	$0$	$0$	$3$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+3q^{7}+6q^{9}+6q^{11}+\cdots$
3328.2.a.l	$3328$	$2$	3328.a	1.a	$1$	$1$	$1$	$26.574$	$\Q$	$_{}$	None	None	✓				1664.2.b.a	$1$	$0$	$0$	$3$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}-3q^{7}+6q^{9}+6q^{11}+\cdots$
3328.2.a.m	$3328$	$2$	3328.a	1.a	$1$	$2$	$2$	$26.574$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				104.2.b.b	$1$	$1$	$0$	$-4$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2\beta q^{5}+(-3+\beta )q^{7}+q^{9}+\cdots$
3328.2.a.n	$3328$	$2$	3328.a	1.a	$1$	$2$	$2$	$26.574$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				104.2.b.b	$1$	$1$	$0$	$-4$	$0$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2\beta q^{5}+(3-\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
3328.2.a.o	$3328$	$2$	3328.a	1.a	$1$	$2$	$2$	$26.574$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1664.2.b.e	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
3328.2.a.p	$3328$	$2$	3328.a	1.a	$1$	$2$	$2$	$26.574$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				832.2.b.a	$1$	$0$	$0$	$-2$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-1-2\beta )q^{5}+(3-\beta )q^{7}+\cdots$
3328.2.a.q	$3328$	$2$	3328.a	1.a	$1$	$2$	$2$	$26.574$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				832.2.b.a	$1$	$1$	$0$	$-2$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1+2\beta )q^{5}+(-3+\beta )q^{7}+\cdots$

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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.