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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 133 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
2700.1.b.a	$2700$	$1$	2700.b	15.d	$2$	$2$	$2$	$1.347$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			2700.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-2 i q^{7}-i q^{13}-2 q^{19}-q^{31}+\cdots$
2700.1.b.b	$2700$	$1$	2700.b	15.d	$2$	$2$	$2$	$1.347$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					108.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{7}+i q^{13}+q^{19}+2 q^{31}-i q^{37}+\cdots$
2700.1.c.a	$2700$	$1$	2700.c	4.b	$2$	$2$	$2$	$1.347$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None					540.1.f.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots$
2700.1.c.b	$2700$	$1$	2700.c	4.b	$2$	$2$	$2$	$1.347$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None					540.1.f.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{16}+\cdots$
2700.1.g.a	$2700$	$1$	2700.g	3.b	$2$	$1$	$1$	$1.347$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			2700.1.g.a	$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-2q^{7}+q^{13}+2q^{19}-q^{31}+q^{37}+\cdots$
2700.1.g.b	$2700$	$1$	2700.g	3.b	$2$	$1$	$1$	$1.347$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓				108.1.c.a	$2$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{7}+q^{13}-q^{19}+2q^{31}+q^{37}+\cdots$
2700.1.g.c	$2700$	$1$	2700.g	3.b	$2$	$1$	$1$	$1.347$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			2700.1.g.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$		$q+2q^{7}-q^{13}+2q^{19}-q^{31}-q^{37}+\cdots$
2700.1.l.a	$2700$	$1$	2700.l	5.c	$4$	$4$	$2$	$1.347$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2700.1.l.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{7}+\beta _{3}q^{13}-\beta _{2}q^{19}-2q^{31}+\cdots$
2700.1.l.b	$2700$	$1$	2700.l	5.c	$4$	$4$	$2$	$1.347$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2700.1.l.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{3}q^{13}+2\beta _{2}q^{19}+q^{31}-\beta _{1}q^{37}+\cdots$
2700.1.m.a	$2700$	$1$	2700.m	60.l	$4$	$8$	$4$	$1.347$	$\Q(\zeta_{24})$	$D_{6}$	None	$\Q(\sqrt{3}) $		✓			2700.1.m.a	$16$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q-\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{3}q^{8}+\cdots$
2700.1.m.b	$2700$	$1$	2700.m	60.l	$4$	$8$	$4$	$1.347$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			2700.1.m.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{3}q^{8}+\zeta_{24}^{4}q^{16}+\cdots$
2700.1.t.a	$2700$	$1$	2700.t	36.f	$6$	$4$	$2$	$1.347$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-5}) $	None			✓	✓	180.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots$
2700.1.bb.a	$2700$	$1$	2700.bb	75.j	$10$	$8$	$2$	$1.347$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓	✓	✓	2700.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{3}q^{5}+(-\zeta_{20}+\zeta_{20}^{7})q^{11}+\cdots$
2700.1.be.a	$2700$	$1$	2700.be	180.v	$12$	$8$	$2$	$1.347$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-5}) $	None			✓	✓	900.1.bd.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}^{3}-\zeta_{24}^{11}+\cdots)q^{7}+\cdots$
2700.1.bj.a	$2700$	$1$	2700.bj	108.j	$18$	$12$	$2$	$1.347$	$\Q(\zeta_{36})$	$D_{9}$	$\Q(\sqrt{-5}) $	None			✓	✓	540.1.bf.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{11}q^{2}+\zeta_{36}q^{3}-\zeta_{36}^{4}q^{4}+\cdots$
2700.1.ca.a	$2700$	$1$	2700.ca	540.ag	$36$	$24$	$2$	$1.347$	$\Q(\zeta_{72})$	$D_{18}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	2700.1.ca.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{72}^{29}q^{2}+\zeta_{72}^{19}q^{3}-\zeta_{72}^{22}q^{4}+\cdots$
2700.2.a.a	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			2700.2.a.a	$2$	$0$	$0$	$0$	$0$	$-5$	$-$	$1$	$N(\mathrm{U}(1))$	$q-5q^{7}-2q^{13}-q^{19}+11q^{31}-11q^{37}+\cdots$
2700.2.a.b	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				108.2.a.a	$2$	$1$	$0$	$0$	$0$	$-5$	$+$	$1$	$N(\mathrm{U}(1))$	$q-5q^{7}+7q^{13}-q^{19}-4q^{31}+q^{37}+\cdots$
2700.2.a.c	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			2700.2.a.c	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$N(\mathrm{U}(1))$	$q-4q^{7}-7q^{13}+8q^{19}-7q^{31}+11q^{37}+\cdots$
2700.2.a.d	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓	✓			2700.2.a.d	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{11}+q^{13}+6q^{17}+2q^{19}+\cdots$
2700.2.a.e	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.d.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-2q^{11}+6q^{13}-q^{17}-3q^{19}+\cdots$
2700.2.a.f	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.a.c	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-2q^{13}-3q^{17}+5q^{19}+3q^{23}+\cdots$
2700.2.a.g	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.a.c	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-2q^{13}+3q^{17}+5q^{19}-3q^{23}+\cdots$
2700.2.a.h	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.d.a	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{11}+6q^{13}+q^{17}-3q^{19}+\cdots$
2700.2.a.i	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓	✓			2700.2.a.d	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+3q^{11}+q^{13}-6q^{17}+2q^{19}+\cdots$
2700.2.a.j	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			2700.2.a.j	$2$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$N(\mathrm{U}(1))$	$q-q^{7}+2q^{13}-7q^{19}-7q^{31}-q^{37}+\cdots$
2700.2.a.k	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-6q^{11}+q^{13}-q^{19}+6q^{23}+\cdots$
2700.2.a.l	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			2700.2.a.j	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$N(\mathrm{U}(1))$	$q+q^{7}-2q^{13}-7q^{19}-7q^{31}+q^{37}+\cdots$
2700.2.a.m	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+6q^{11}+q^{13}-q^{19}-6q^{23}+\cdots$
2700.2.a.n	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓	✓			2700.2.a.d	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{11}-q^{13}-6q^{17}+2q^{19}+\cdots$
2700.2.a.o	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.d.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-2q^{11}-6q^{13}+q^{17}-3q^{19}+\cdots$
2700.2.a.p	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.d.a	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+2q^{11}-6q^{13}-q^{17}-3q^{19}+\cdots$
2700.2.a.q	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓	✓			2700.2.a.d	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+3q^{11}-q^{13}+6q^{17}+2q^{19}+\cdots$
2700.2.a.r	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.a.a	$1$	$1$	$0$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-6q^{11}+4q^{13}-3q^{17}-7q^{19}+\cdots$
2700.2.a.s	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			2700.2.a.c	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{7}+7q^{13}+8q^{19}-7q^{31}-11q^{37}+\cdots$
2700.2.a.t	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	None	None	✓				540.2.a.a	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}+6q^{11}+4q^{13}+3q^{17}-7q^{19}+\cdots$
2700.2.a.u	$2700$	$2$	2700.a	1.a	$1$	$1$	$1$	$21.560$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			2700.2.a.a	$2$	$0$	$0$	$0$	$0$	$5$	$-$	$1$	$N(\mathrm{U}(1))$	$q+5q^{7}+2q^{13}-q^{19}+11q^{31}+11q^{37}+\cdots$
2700.2.a.v	$2700$	$2$	2700.a	1.a	$1$	$2$	$2$	$21.560$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓		✓		540.2.d.c	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-\beta q^{11}-3q^{13}+2\beta q^{17}+3q^{19}+\cdots$
2700.2.a.w	$2700$	$2$	2700.a	1.a	$1$	$2$	$2$	$21.560$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓		✓		540.2.d.c	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-\beta q^{11}+3q^{13}-2\beta q^{17}+3q^{19}+\cdots$
2700.2.d.a	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	None	None					540.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{7}-6 q^{11}-i q^{13}+q^{19}-6 i q^{23}+\cdots$
2700.2.d.b	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	None	None					540.2.a.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4 i q^{7}-6 q^{11}-4 i q^{13}-3 i q^{17}+\cdots$
2700.2.d.c	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2700.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{7}-3 q^{11}+i q^{13}-6 i q^{17}+\cdots$
2700.2.d.d	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			2700.2.a.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4 i q^{7}-7 i q^{13}-8 q^{19}-7 q^{31}+\cdots$
2700.2.d.e	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	None	None					540.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{7}-2 i q^{13}+3 i q^{17}-5 q^{19}+\cdots$
2700.2.d.f	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	None	None					540.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{7}-2 i q^{13}-3 i q^{17}-5 q^{19}+\cdots$
2700.2.d.g	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None					108.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+5 i q^{7}+7 i q^{13}+q^{19}-4 q^{31}+\cdots$
2700.2.d.h	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			2700.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+5 i q^{7}-2 i q^{13}+q^{19}+11 q^{31}+\cdots$
2700.2.d.i	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			2700.2.a.j	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+i q^{7}+2 i q^{13}+7 q^{19}-7 q^{31}+\cdots$
2700.2.d.j	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2700.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{7}+3 q^{11}+i q^{13}+6 i q^{17}+\cdots$
2700.2.d.k	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	$\Q(\sqrt{-1}) $	$_{}$	None	None					540.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{7}+6 q^{11}-i q^{13}+q^{19}+6 i q^{23}+\cdots$

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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.