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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 85 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
3960.1.b.a	$3960$	$1$	3960.b	1320.b	$2$	$4$	$4$	$1.976$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-10}) $	None		✓			3960.1.b.a	$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
3960.1.b.b	$3960$	$1$	3960.b	1320.b	$2$	$4$	$4$	$1.976$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-10}) $	None		✓			3960.1.b.a	$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
3960.1.b.c	$3960$	$1$	3960.b	1320.b	$2$	$8$	$8$	$1.976$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		✓			3960.1.b.c	$8$	$0$	$0$	$0$	$-8$	$0$		$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}-q^{5}+(\zeta_{16}^{3}+\cdots)q^{7}+\cdots$
3960.1.b.d	$3960$	$1$	3960.b	1320.b	$2$	$8$	$8$	$1.976$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		✓			3960.1.b.c	$8$	$0$	$0$	$0$	$8$	$0$		$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+q^{5}+(-\zeta_{16}^{3}+\cdots)q^{7}+\cdots$
3960.1.x.a	$3960$	$1$	3960.x	440.o	$2$	$1$	$1$	$1.976$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓				440.1.o.a	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
3960.1.x.b	$3960$	$1$	3960.x	440.o	$2$	$1$	$1$	$1.976$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓				440.1.o.a	$2$	$0$	$-1$	$0$	$1$	$-1$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
3960.1.x.c	$3960$	$1$	3960.x	440.o	$2$	$1$	$1$	$1.976$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓				440.1.o.a	$2$	$0$	$1$	$0$	$-1$	$1$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
3960.1.x.d	$3960$	$1$	3960.x	440.o	$2$	$1$	$1$	$1.976$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓				440.1.o.a	$2$	$0$	$1$	$0$	$1$	$1$		$1$		$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
3960.1.x.e	$3960$	$1$	3960.x	440.o	$2$	$2$	$2$	$1.976$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-55}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{66}) $		✓			3960.1.x.e	$8$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-i q^{5}-q^{8}+i q^{10}+\cdots$
3960.1.x.f	$3960$	$1$	3960.x	440.o	$2$	$2$	$2$	$1.976$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{330}) $		✓			3960.1.x.f	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+i q^{2}-q^{4}-i q^{5}-2 q^{7}-i q^{8}+\cdots$
3960.1.x.g	$3960$	$1$	3960.x	440.o	$2$	$2$	$2$	$1.976$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{330}) $		✓			3960.1.x.f	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-i q^{2}-q^{4}-i q^{5}+2 q^{7}+i q^{8}+\cdots$
3960.1.x.h	$3960$	$1$	3960.x	440.o	$2$	$2$	$2$	$1.976$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-55}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{66}) $		✓			3960.1.x.e	$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-i q^{5}+q^{8}-i q^{10}+\cdots$
3960.1.x.i	$3960$	$1$	3960.x	440.o	$2$	$4$	$4$	$1.976$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None			✓		440.1.o.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
3960.1.bp.a	$3960$	$1$	3960.bp	440.w	$4$	$8$	$4$	$1.976$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-66}) $	None		✓			3960.1.bp.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots$
3960.1.bp.b	$3960$	$1$	3960.bp	440.w	$4$	$8$	$4$	$1.976$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-66}) $	None		✓			3960.1.bp.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{3}q^{5}+\cdots$
3960.1.cd.a	$3960$	$1$	3960.cd	495.o	$6$	$8$	$4$	$1.976$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	3960.1.cd.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+\zeta_{24}^{6}q^{3}+\zeta_{24}^{10}q^{5}+(-\zeta_{24}^{5}+\cdots)q^{7}+\cdots$
3960.1.cm.a	$3960$	$1$	3960.cm	3960.bm	$6$	$6$	$3$	$1.976$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-110}) $	None		✓			3960.1.cm.a	$4$	$0$	$-3$	$0$	$-3$	$0$		$1$		$q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{8}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
3960.1.cm.b	$3960$	$1$	3960.cm	3960.bm	$6$	$6$	$3$	$1.976$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-110}) $	None		✓			3960.1.cm.a	$4$	$0$	$-3$	$0$	$3$	$0$		$1$		$q+\zeta_{18}^{6}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
3960.1.cm.c	$3960$	$1$	3960.cm	3960.bm	$6$	$6$	$3$	$1.976$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-110}) $	None		✓			3960.1.cm.a	$4$	$0$	$3$	$0$	$-3$	$0$		$1$		$q-\zeta_{18}^{6}q^{2}+\zeta_{18}^{8}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
3960.1.cm.d	$3960$	$1$	3960.cm	3960.bm	$6$	$6$	$3$	$1.976$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-110}) $	None		✓			3960.1.cm.a	$4$	$0$	$3$	$0$	$3$	$0$		$1$		$q-\zeta_{18}^{6}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
3960.1.dh.a	$3960$	$1$	3960.dh	440.ah	$10$	$4$	$1$	$1.976$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None					440.1.bh.a	$4$	$0$	$-1$	$0$	$-1$	$-3$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(-1+\cdots)q^{7}+\cdots$
3960.1.dh.b	$3960$	$1$	3960.dh	440.ah	$10$	$4$	$1$	$1.976$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None					440.1.bh.a	$4$	$0$	$1$	$0$	$1$	$3$		$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+(1+\cdots)q^{7}+\cdots$
3960.1.dh.c	$3960$	$1$	3960.dh	440.ah	$10$	$8$	$2$	$1.976$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-10}) $	None		✓			3960.1.dh.c	$8$	$0$	$-2$	$0$	$2$	$0$		$1$		$q-\zeta_{20}^{2}q^{2}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{8}q^{5}+\cdots$
3960.1.dh.d	$3960$	$1$	3960.dh	440.ah	$10$	$8$	$2$	$1.976$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-10}) $	None		✓			3960.1.dh.c	$8$	$0$	$2$	$0$	$-2$	$0$		$1$		$q+\zeta_{20}^{2}q^{2}+\zeta_{20}^{4}q^{4}+\zeta_{20}^{8}q^{5}+\cdots$
3960.1.dk.a	$3960$	$1$	3960.dk	440.aa	$10$	$8$	$2$	$1.976$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-30}) $	None		✓			3960.1.dk.a	$8$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}+\zeta_{20}^{9}q^{5}+\cdots$
3960.1.dk.b	$3960$	$1$	3960.dk	440.aa	$10$	$8$	$2$	$1.976$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓			3960.1.dk.b	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}q^{5}+(-\zeta_{20}^{6}+\cdots)q^{7}+\cdots$
3960.1.dk.c	$3960$	$1$	3960.dk	440.aa	$10$	$8$	$2$	$1.976$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓			3960.1.dk.b	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{7}q^{5}+(\zeta_{20}^{6}+\cdots)q^{7}+\cdots$
3960.1.dk.d	$3960$	$1$	3960.dk	440.aa	$10$	$8$	$2$	$1.976$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-30}) $	None		✓			3960.1.dk.a	$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}+\zeta_{20}^{9}q^{5}+\cdots$
3960.1.eg.a	$3960$	$1$	3960.eg	1320.ca	$10$	$16$	$4$	$1.976$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-10}) $	None		✓			3960.1.eg.a	$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{16}q^{2}-\zeta_{40}^{12}q^{4}+\zeta_{40}^{14}q^{5}+\cdots$
3960.1.eg.b	$3960$	$1$	3960.eg	1320.ca	$10$	$16$	$4$	$1.976$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-10}) $	None		✓			3960.1.eg.a	$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{16}q^{2}-\zeta_{40}^{12}q^{4}-\zeta_{40}^{14}q^{5}+\cdots$
3960.1.ez.a	$3960$	$1$	3960.ez	440.ap	$20$	$16$	$2$	$1.976$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-6}) $	None		✓			3960.1.ez.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{40}^{9}q^{2}+\zeta_{40}^{18}q^{4}-\zeta_{40}^{3}q^{5}+\cdots$
3960.1.ez.b	$3960$	$1$	3960.ez	440.ap	$20$	$16$	$2$	$1.976$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-6}) $	None		✓			3960.1.ez.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{40}^{9}q^{2}+\zeta_{40}^{18}q^{4}-\zeta_{40}^{19}q^{5}+\cdots$
3960.2.a.a	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.m	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-q^{11}-6q^{13}+2q^{17}+\cdots$
3960.2.a.b	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.e	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}+q^{11}+2q^{13}-6q^{17}+\cdots$
3960.2.a.c	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.g	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{11}-6q^{13}+6q^{17}+q^{25}+\cdots$
3960.2.a.d	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.n	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots$
3960.2.a.e	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.f	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{11}-2q^{13}+6q^{17}-4q^{19}+\cdots$
3960.2.a.f	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				440.2.a.d	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+q^{11}-6q^{13}-3q^{17}+\cdots$
3960.2.a.g	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.h	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-q^{11}+2q^{13}+2q^{17}+\cdots$
3960.2.a.h	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓	✓			3960.2.a.h	$1$	$1$	$0$	$0$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}+q^{11}-4q^{13}+2q^{17}+\cdots$
3960.2.a.i	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				440.2.a.c	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}+q^{11}+6q^{13}+6q^{17}+\cdots$
3960.2.a.j	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				440.2.a.b	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-q^{11}-4q^{13}+4q^{17}+\cdots$
3960.2.a.k	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.k	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-q^{11}+8q^{17}-8q^{19}+\cdots$
3960.2.a.l	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.b	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-q^{11}+4q^{13}-4q^{19}+\cdots$
3960.2.a.m	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.i	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+q^{11}-4q^{13}-4q^{17}+\cdots$
3960.2.a.n	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.a	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+q^{11}-4q^{13}+4q^{17}+\cdots$
3960.2.a.o	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.j	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+q^{11}-4q^{17}+4q^{19}+\cdots$
3960.2.a.p	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				440.2.a.a	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+q^{11}-8q^{19}+8q^{23}+\cdots$
3960.2.a.q	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.l	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-q^{11}-4q^{17}-4q^{19}+\cdots$
3960.2.a.r	$3960$	$2$	3960.a	1.a	$1$	$1$	$1$	$31.621$	$\Q$	$_{}$	None	None	✓				1320.2.a.c	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+q^{11}-4q^{13}-4q^{19}+\cdots$

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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.