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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 274 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
147.1.l.a	$147$	$1$	147.l	147.l	$14$	$6$	$1$	$0.073$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3})$	None		✓	✓	✓	147.1.l.a	$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots$
147.2.a.a	$147$	$2$	147.a	1.a	$1$	$1$	$1$	$1.174$	$\Q$	$_{}$	None	None	✓				21.2.a.a	$1$	$0$	$-1$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+3q^{8}+\cdots$
147.2.a.b	$147$	$2$	147.a	1.a	$1$	$1$	$1$	$1.174$	$\Q$	$_{}$	None	None	✓				21.2.e.a	$1$	$0$	$2$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots$
147.2.a.c	$147$	$2$	147.a	1.a	$1$	$1$	$1$	$1.174$	$\Q$	$_{}$	None	None	✓				21.2.e.a	$1$	$0$	$2$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots$
147.2.a.d	$147$	$2$	147.a	1.a	$1$	$2$	$2$	$1.174$	$\Q(\sqrt{2})$	$_{}$	None	None	✓	✓	✓	✓	147.2.a.d	$1$	$1$	$-2$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
147.2.a.e	$147$	$2$	147.a	1.a	$1$	$2$	$2$	$1.174$	$\Q(\sqrt{2})$	$_{}$	None	None	✓	✓	✓		147.2.a.d	$1$	$0$	$-2$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(2+\cdots)q^{5}+\cdots$
147.2.c.a	$147$	$2$	147.c	21.c	$2$	$2$	$2$	$1.174$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None					21.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}+2 q^{4}-3 q^{9}-2\beta q^{12}+\cdots$
147.2.c.b	$147$	$2$	147.c	21.c	$2$	$8$	$8$	$1.174$	8.0.3288334336.2	$_{}$	None	None		✓	✓		147.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
147.2.e.a	$147$	$2$	147.e	7.c	$3$	$2$	$1$	$1.174$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.2.e.a	$2$	$0$	$-2$	$1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
147.2.e.b	$147$	$2$	147.e	7.c	$3$	$2$	$1$	$1.174$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.2.a.a	$2$	$0$	$1$	$-1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
147.2.e.c	$147$	$2$	147.e	7.c	$3$	$2$	$1$	$1.174$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.2.a.a	$2$	$0$	$1$	$1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
147.2.e.d	$147$	$2$	147.e	7.c	$3$	$4$	$2$	$1.174$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			147.2.a.d	$2$	$0$	$2$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
147.2.e.e	$147$	$2$	147.e	7.c	$3$	$4$	$2$	$1.174$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			147.2.a.d	$2$	$0$	$2$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
147.2.g.a	$147$	$2$	147.g	21.g	$6$	$2$	$1$	$1.174$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None					21.2.g.a	$4$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{9}+\cdots$
147.2.g.b	$147$	$2$	147.g	21.g	$6$	$16$	$8$	$1.174$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		147.2.c.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{13}q^{2}+(\beta _{7}-\beta _{9})q^{3}+(1-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
147.2.i.a	$147$	$2$	147.i	49.e	$7$	$24$	$4$	$1.174$		$_{}$	None	None		✓			147.2.i.a	$2$	$0$	$1$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{7}]$
147.2.i.b	$147$	$2$	147.i	49.e	$7$	$36$	$6$	$1.174$		$_{}$	None	None		✓	✓		147.2.i.b	$2$	$0$	$-1$	$-6$	$-4$	$-6$			$\mathrm{SU}(2)[C_{7}]$
147.2.k.a	$147$	$2$	147.k	147.k	$14$	$96$	$16$	$1.174$		$_{}$	None	None		✓	✓	✓	147.2.k.a	$4$	$0$	$0$	$-7$	$0$	$-14$			$\mathrm{SU}(2)[C_{14}]$
147.2.m.a	$147$	$2$	147.m	49.g	$21$	$48$	$4$	$1.174$		$_{}$	None	None		✓			147.2.m.a	$2$	$0$	$-1$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{21}]$
147.2.m.b	$147$	$2$	147.m	49.g	$21$	$60$	$5$	$1.174$		$_{}$	None	None		✓	✓		147.2.m.b	$2$	$0$	$1$	$5$	$-2$	$5$			$\mathrm{SU}(2)[C_{21}]$
147.2.o.a	$147$	$2$	147.o	147.o	$42$	$12$	$1$	$1.174$	$\Q(\zeta_{21})$	$_{}$	$\Q(\sqrt{-3})$	None		✓			147.2.o.a	$4$	$0$	$0$	$3$	$0$	$-1$		$1$	$\mathrm{U}(1)[D_{42}]$	$q+(2\zeta_{21}+\zeta_{21}^{8})q^{3}+(-2\zeta_{21}^{3}-2\zeta_{21}^{10}+\cdots)q^{4}+\cdots$
147.2.o.b	$147$	$2$	147.o	147.o	$42$	$192$	$16$	$1.174$		$_{}$	None	None		✓	✓		147.2.o.b	$4$	$0$	$0$	$-14$	$0$	$-28$			$\mathrm{SU}(2)[C_{42}]$
147.3.b.a	$147$	$3$	147.b	3.b	$2$	$1$	$1$	$4.005$	$\Q$	$_{}$	$\Q(\sqrt{-3})$	None	✓				21.3.h.a	$2$	$0$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+4q^{4}+9q^{9}-12q^{12}+23q^{13}+\cdots$
147.3.b.b	$147$	$3$	147.b	3.b	$2$	$1$	$1$	$4.005$	$\Q$	$_{}$	$\Q(\sqrt{-3})$	None	✓				21.3.h.a	$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+4q^{4}+9q^{9}+12q^{12}-23q^{13}+\cdots$
147.3.b.c	$147$	$3$	147.b	3.b	$2$	$2$	$2$	$4.005$	$\Q(\sqrt{-5})$	$_{}$	None	None					21.3.h.b	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}+\beta q^{5}+\cdots$
147.3.b.d	$147$	$3$	147.b	3.b	$2$	$2$	$2$	$4.005$	$\Q(\sqrt{-5})$	$_{}$	None	None					21.3.h.b	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(2+\beta )q^{3}-q^{4}-\beta q^{5}+(-5+\cdots)q^{6}+\cdots$
147.3.b.e	$147$	$3$	147.b	3.b	$2$	$4$	$4$	$4.005$	$\Q(\sqrt{-5}, \sqrt{-6})$	$_{}$	None	None		✓			147.3.b.e	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
147.3.b.f	$147$	$3$	147.b	3.b	$2$	$4$	$4$	$4.005$	4.0.65856.1	$_{}$	None	None					21.3.b.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots$
147.3.b.g	$147$	$3$	147.b	3.b	$2$	$8$	$8$	$4.005$	8.0. $\cdots$ .7	$_{}$	None	None		✓	✓		147.3.b.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{5}-\beta _{7})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots$
147.3.d.a	$147$	$3$	147.d	7.b	$2$	$2$	$2$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.3.f.c	$2$	$0$	$-4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2 q^{2}-\beta q^{3}+2\beta q^{5}+2\beta q^{6}+\cdots$
147.3.d.b	$147$	$3$	147.d	7.b	$2$	$2$	$2$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.3.f.b	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta q^{3}-3 q^{4}+3\beta q^{5}+\beta q^{6}+\cdots$
147.3.d.c	$147$	$3$	147.d	7.b	$2$	$2$	$2$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.3.f.a	$2$	$0$	$6$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+3 q^{2}+\beta q^{3}+5 q^{4}+3\beta q^{5}+3\beta q^{6}+\cdots$
147.3.d.d	$147$	$3$	147.d	7.b	$2$	$8$	$8$	$4.005$	8.0.339738624.1	$_{}$	None	None		✓	✓		147.3.d.d	$2$	$0$	$-8$	$0$	$0$	$0$		$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{2})q^{2}+\beta _{3}q^{3}+(5-\beta _{5})q^{4}+\cdots$
147.3.f.a	$147$	$3$	147.f	7.d	$6$	$2$	$1$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.3.f.a	$2$	$0$	$-3$	$3$	$-9$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-3\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots$
147.3.f.b	$147$	$3$	147.f	7.d	$6$	$2$	$1$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.3.d.a	$2$	$0$	$-1$	$-3$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots$
147.3.f.c	$147$	$3$	147.f	7.d	$6$	$2$	$1$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.3.f.b	$2$	$0$	$-1$	$-3$	$9$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots$
147.3.f.d	$147$	$3$	147.f	7.d	$6$	$2$	$1$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.3.d.a	$2$	$0$	$-1$	$3$	$12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots$
147.3.f.e	$147$	$3$	147.f	7.d	$6$	$2$	$1$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	None	None					21.3.f.c	$2$	$0$	$2$	$3$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+\cdots$
147.3.f.f	$147$	$3$	147.f	7.d	$6$	$8$	$4$	$4.005$	8.0.339738624.1	$_{}$	None	None		✓			147.3.d.d	$2$	$0$	$4$	$-12$	$0$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{7})q^{2}+(-1+\beta _{3})q^{3}+(-5+\cdots)q^{4}+\cdots$
147.3.f.g	$147$	$3$	147.f	7.d	$6$	$8$	$4$	$4.005$	8.0.339738624.1	$_{}$	None	None		✓			147.3.d.d	$2$	$0$	$4$	$12$	$0$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{7})q^{2}+(1-\beta _{3})q^{3}+(-5+\cdots)q^{4}+\cdots$
147.3.h.a	$147$	$3$	147.h	21.h	$6$	$2$	$1$	$4.005$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None					21.3.h.a	$4$	$0$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-9+9\zeta_{6})q^{9}+\cdots$
147.3.h.b	$147$	$3$	147.h	21.h	$6$	$4$	$2$	$4.005$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	None	None					21.3.h.b	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$
147.3.h.c	$147$	$3$	147.h	21.h	$6$	$8$	$4$	$4.005$	8.0. $\cdots$ .8	$_{}$	None	None					21.3.b.a	$4$	$0$	$0$	$-2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+(\beta _{2}-\beta _{6})q^{3}+(2\beta _{2}-3\beta _{4}+\cdots)q^{4}+\cdots$
147.3.h.d	$147$	$3$	147.h	21.h	$6$	$8$	$4$	$4.005$	8.0.3317760000.3	$_{}$	None	None		✓			147.3.b.e	$8$	$0$	$0$	$0$	$0$	$0$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{6})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$
147.3.h.e	$147$	$3$	147.h	21.h	$6$	$8$	$4$	$4.005$	8.0. $\cdots$ .8	$_{}$	None	None					21.3.b.a	$4$	$0$	$0$	$2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+(-\beta _{2}+\beta _{6})q^{3}+(2\beta _{2}-3\beta _{4}+\cdots)q^{4}+\cdots$
147.3.h.f	$147$	$3$	147.h	21.h	$6$	$16$	$8$	$4.005$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		147.3.b.g	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{8}-\beta _{9}+\beta _{12})q^{3}+(1+\cdots)q^{4}+\cdots$
147.3.j.a	$147$	$3$	147.j	49.f	$14$	$108$	$18$	$4.005$		$_{}$	None	None		✓	✓	✓	147.3.j.a	$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{14}]$
147.3.l.a	$147$	$3$	147.l	147.l	$14$	$216$	$36$	$4.005$		$_{}$	None	None		✓	✓	✓	147.3.l.a	$4$	$0$	$0$	$-5$	$0$	$-14$			$\mathrm{SU}(2)[C_{14}]$
147.3.n.a	$147$	$3$	147.n	147.n	$42$	$12$	$1$	$4.005$	$\Q(\zeta_{21})$	$_{}$	$\Q(\sqrt{-3})$	None		✓			147.3.n.a	$4$	$0$	$0$	$-3$	$0$	$13$		$1$	$\mathrm{U}(1)[D_{42}]$	$q+(3\zeta_{21}^{2}+3\zeta_{21}^{9})q^{3}+(-4+4\zeta_{21}^{2}+\cdots)q^{4}+\cdots$
147.3.n.b	$147$	$3$	147.n	147.n	$42$	$408$	$34$	$4.005$		$_{}$	None	None		✓	✓		147.3.n.b	$4$	$0$	$0$	$-10$	$0$	$-42$			$\mathrm{SU}(2)[C_{42}]$

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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.