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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 124 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
1248.1.b.a	$1248$	$1$	1248.b	312.b	$2$	$4$	$4$	$0.623$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None			✓	✓	312.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{9}+\cdots$
1248.1.l.a	$1248$	$1$	1248.l	39.d	$2$	$4$	$4$	$0.623$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{39}) $		✓	✓	✓	1248.1.l.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
1248.1.bs.a	$1248$	$1$	1248.bs	39.i	$6$	$8$	$4$	$0.623$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1248.1.bs.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{3}-\zeta_{24}^{6}q^{5}+(\zeta_{24}+\zeta_{24}^{7}+\cdots)q^{7}+\cdots$
1248.1.cm.a	$1248$	$1$	1248.cm	1248.bm	$8$	$16$	$4$	$0.623$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-39}) $	None		✓	✓	✓	1248.1.cm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{10}q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
1248.2.a.a	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.a	$1$	$1$	$0$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots$
1248.2.a.b	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.b	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}+q^{13}+\cdots$
1248.2.a.c	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.c	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+q^{13}+2q^{17}+\cdots$
1248.2.a.d	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.d	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots$
1248.2.a.e	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.e	$1$	$0$	$0$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
1248.2.a.f	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.b	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-4q^{11}+q^{13}+\cdots$
1248.2.a.g	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.a	$1$	$1$	$0$	$1$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots$
1248.2.a.h	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.d	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots$
1248.2.a.i	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.c	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+q^{13}+2q^{17}+\cdots$
1248.2.a.j	$1248$	$2$	1248.a	1.a	$1$	$1$	$1$	$9.965$	$\Q$	$_{}$	None	None	✓	✓			1248.2.a.e	$1$	$0$	$0$	$1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
1248.2.a.k	$1248$	$2$	1248.a	1.a	$1$	$2$	$2$	$9.965$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1248.2.a.k	$1$	$0$	$0$	$-2$	$-2$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+(3-\beta )q^{7}+q^{9}+\cdots$
1248.2.a.l	$1248$	$2$	1248.a	1.a	$1$	$2$	$2$	$9.965$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1248.2.a.l	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+(-1-\beta )q^{7}+q^{9}+\cdots$
1248.2.a.m	$1248$	$2$	1248.a	1.a	$1$	$2$	$2$	$9.965$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1248.2.a.k	$1$	$1$	$0$	$2$	$-2$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+(-3+\beta )q^{7}+\cdots$
1248.2.a.n	$1248$	$2$	1248.a	1.a	$1$	$2$	$2$	$9.965$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1248.2.a.l	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots$
1248.2.a.o	$1248$	$2$	1248.a	1.a	$1$	$3$	$3$	$9.965$	3.3.148.1	$_{}$	None	None	✓	✓	✓		1248.2.a.o	$1$	$0$	$0$	$-3$	$2$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
1248.2.a.p	$1248$	$2$	1248.a	1.a	$1$	$3$	$3$	$9.965$	3.3.148.1	$_{}$	None	None	✓	✓	✓		1248.2.a.o	$1$	$0$	$0$	$3$	$2$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
1248.2.c.a	$1248$	$2$	1248.c	13.b	$2$	$6$	$6$	$9.965$	6.0.153664.1	$_{}$	None	None		✓			1248.2.c.a	$2$	$0$	$0$	$-6$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
1248.2.c.b	$1248$	$2$	1248.c	13.b	$2$	$6$	$6$	$9.965$	6.0.153664.1	$_{}$	None	None		✓			1248.2.c.a	$2$	$0$	$0$	$6$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
1248.2.c.c	$1248$	$2$	1248.c	13.b	$2$	$8$	$8$	$9.965$	8.0.134560000.4	$_{}$	None	None		✓			1248.2.c.c	$2$	$0$	$0$	$-8$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
1248.2.c.d	$1248$	$2$	1248.c	13.b	$2$	$8$	$8$	$9.965$	8.0.134560000.4	$_{}$	None	None		✓			1248.2.c.c	$2$	$0$	$0$	$8$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+\beta _{6}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots$
1248.2.d.a	$1248$	$2$	1248.d	12.b	$2$	$4$	$4$	$9.965$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1248.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{3}+(-\beta_{2}+\beta_1)q^{7}+(\beta_{3}+1)q^{9}+\cdots$
1248.2.d.b	$1248$	$2$	1248.d	12.b	$2$	$8$	$8$	$9.965$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			1248.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{6} q^{3}+\beta_{2} q^{5}+\beta_{5} q^{7}+(-\beta_1+1)q^{9}+\cdots$
1248.2.d.c	$1248$	$2$	1248.d	12.b	$2$	$16$	$16$	$9.965$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1248.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$
1248.2.d.d	$1248$	$2$	1248.d	12.b	$2$	$20$	$20$	$9.965$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		1248.2.d.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{23}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+\beta _{15}q^{5}+\beta _{7}q^{7}-\beta _{16}q^{9}+\cdots$
1248.2.g.a	$1248$	$2$	1248.g	8.b	$2$	$8$	$8$	$9.965$	$\Q(\zeta_{20})$	$_{}$	None	None					312.2.g.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+(\beta_{2}-\beta_1)q^{5}+(-\beta_{5}-1)q^{7}+\cdots$
1248.2.g.b	$1248$	$2$	1248.g	8.b	$2$	$16$	$16$	$9.965$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓		312.2.g.b	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+\beta _{12}q^{5}-\beta _{5}q^{7}-q^{9}+\beta _{10}q^{11}+\cdots$
1248.2.h.a	$1248$	$2$	1248.h	312.h	$2$	$8$	$8$	$9.965$	8.0.$\cdots$.21	$_{}$	$\Q(\sqrt{-39}) $	None					312.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}-\beta _{4}q^{5}+3q^{9}+(-\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots$
1248.2.h.b	$1248$	$2$	1248.h	312.h	$2$	$12$	$12$	$9.965$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-26}) $	None					312.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{5}q^{3}+\beta _{9}q^{5}+(-\beta _{1}+\beta _{11})q^{7}+\cdots$
1248.2.h.c	$1248$	$2$	1248.h	312.h	$2$	$32$	$32$	$9.965$		$_{}$	None	None			✓		312.2.h.c	$8$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1248.2.j.a	$1248$	$2$	1248.j	24.f	$2$	$48$	$48$	$9.965$		$_{}$	None	None			✓	✓	312.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1248.2.m.a	$1248$	$2$	1248.m	104.e	$2$	$2$	$2$	$9.965$	$\Q(\sqrt{-1}) $	$_{}$	None	None					312.2.m.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-2 q^{5}-q^{9}+4 q^{11}+(-2 i+3)q^{13}+\cdots$
1248.2.m.b	$1248$	$2$	1248.m	104.e	$2$	$2$	$2$	$9.965$	$\Q(\sqrt{-1}) $	$_{}$	None	None					312.2.m.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 q^{5}-q^{9}-4 q^{11}+(2 i-3)q^{13}+\cdots$
1248.2.m.c	$1248$	$2$	1248.m	104.e	$2$	$24$	$24$	$9.965$		$_{}$	None	None			✓		312.2.m.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1248.2.n.a	$1248$	$2$	1248.n	156.h	$2$	$4$	$4$	$9.965$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1248.2.n.a	$2$	$0$	$0$	$-4$	$-8$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{2}-1)q^{3}+(\beta_{3}-2)q^{5}+(-\beta_{3}+2)q^{7}+\cdots$
1248.2.n.b	$1248$	$2$	1248.n	156.h	$2$	$4$	$4$	$9.965$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1248.2.n.a	$2$	$0$	$0$	$-4$	$8$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}-1)q^{3}+(\beta_{3}+2)q^{5}+(-\beta_{3}-2)q^{7}+\cdots$
1248.2.n.c	$1248$	$2$	1248.n	156.h	$2$	$4$	$4$	$9.965$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1248.2.n.a	$2$	$0$	$0$	$4$	$-8$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}+1)q^{3}+(\beta_{3}-2)q^{5}+(\beta_{3}-2)q^{7}+\cdots$
1248.2.n.d	$1248$	$2$	1248.n	156.h	$2$	$4$	$4$	$9.965$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1248.2.n.a	$2$	$0$	$0$	$4$	$8$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{2}+1)q^{3}+(-\beta_{3}+2)q^{5}+\cdots$
1248.2.n.e	$1248$	$2$	1248.n	156.h	$2$	$40$	$40$	$9.965$		$_{}$	None	None		✓	✓		1248.2.n.e	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1248.2.q.a	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1248.2.q.a	$2$	$0$	$0$	$-1$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(6+\cdots)q^{11}+\cdots$
1248.2.q.b	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1248.2.q.b	$2$	$0$	$0$	$-1$	$6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+3q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1248.2.q.c	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1248.2.q.c	$2$	$0$	$0$	$-1$	$8$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+4q^{5}-3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1248.2.q.d	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1248.2.q.a	$2$	$0$	$0$	$1$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots$
1248.2.q.e	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1248.2.q.b	$2$	$0$	$0$	$1$	$6$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+3q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1248.2.q.f	$1248$	$2$	1248.q	13.c	$3$	$2$	$1$	$9.965$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1248.2.q.c	$2$	$0$	$0$	$1$	$8$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+4q^{5}+3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1248.2.q.g	$1248$	$2$	1248.q	13.c	$3$	$4$	$2$	$9.965$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			1248.2.q.g	$2$	$0$	$0$	$-2$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
1248.2.q.h	$1248$	$2$	1248.q	13.c	$3$	$4$	$2$	$9.965$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		✓			1248.2.q.h	$2$	$0$	$0$	$-2$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{3}+\beta _{3}q^{5}+(\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots$

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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.