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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 269 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
525.1.k.a	$525$	$1$	525.k	105.k	$4$	$4$	$2$	$0.262$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{105}) $		✓	✓	✓	525.1.k.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
525.1.p.a	$525$	$1$	525.p	105.o	$6$	$4$	$2$	$0.262$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	525.1.u.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
525.1.u.a	$525$	$1$	525.u	21.h	$6$	$2$	$1$	$0.262$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			525.1.u.a	$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
525.1.u.b	$525$	$1$	525.u	21.h	$6$	$2$	$1$	$0.262$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			525.1.u.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
525.1.be.a	$525$	$1$	525.be	105.w	$12$	$8$	$2$	$0.262$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	525.1.be.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+\cdots$
525.2.a.a	$525$	$2$	525.a	1.a	$1$	$1$	$1$	$4.192$	$\Q$	$_{}$	None	None	✓				105.2.a.a	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots$
525.2.a.b	$525$	$2$	525.a	1.a	$1$	$1$	$1$	$4.192$	$\Q$	$_{}$	None	None	✓		✓	✓	105.2.d.a	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots$
525.2.a.c	$525$	$2$	525.a	1.a	$1$	$1$	$1$	$4.192$	$\Q$	$_{}$	None	None	✓				105.2.d.a	$1$	$1$	$1$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots$
525.2.a.d	$525$	$2$	525.a	1.a	$1$	$1$	$1$	$4.192$	$\Q$	$_{}$	None	None	✓		✓	✓	21.2.a.a	$1$	$0$	$1$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots$
525.2.a.e	$525$	$2$	525.a	1.a	$1$	$2$	$2$	$4.192$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		525.2.a.e	$1$	$1$	$-3$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots$
525.2.a.f	$525$	$2$	525.a	1.a	$1$	$2$	$2$	$4.192$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	✓		525.2.a.f	$1$	$1$	$-1$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots$
525.2.a.g	$525$	$2$	525.a	1.a	$1$	$2$	$2$	$4.192$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				105.2.a.b	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-q^{7}-\beta q^{8}+\cdots$
525.2.a.h	$525$	$2$	525.a	1.a	$1$	$2$	$2$	$4.192$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			525.2.a.f	$1$	$0$	$1$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots$
525.2.a.i	$525$	$2$	525.a	1.a	$1$	$2$	$2$	$4.192$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			525.2.a.e	$1$	$0$	$3$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots$
525.2.a.j	$525$	$2$	525.a	1.a	$1$	$3$	$3$	$4.192$	3.3.148.1	$_{}$	None	None	✓		✓		105.2.d.b	$1$	$0$	$-1$	$3$	$0$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
525.2.a.k	$525$	$2$	525.a	1.a	$1$	$3$	$3$	$4.192$	3.3.148.1	$_{}$	None	None	✓		✓	✓	105.2.d.b	$1$	$0$	$1$	$-3$	$0$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
525.2.b.a	$525$	$2$	525.b	21.c	$2$	$2$	$2$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.b.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-\beta q^{3}-q^{4}-3 q^{6}+(\beta-2)q^{7}+\cdots$
525.2.b.b	$525$	$2$	525.b	21.c	$2$	$2$	$2$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.b.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+\beta q^{3}-q^{4}+3 q^{6}+(-\beta-2)q^{7}+\cdots$
525.2.b.c	$525$	$2$	525.b	21.c	$2$	$2$	$2$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			525.2.b.c	$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1-2\zeta_{6})q^{3}+2q^{4}+(-2-\zeta_{6})q^{7}+\cdots$
525.2.b.d	$525$	$2$	525.b	21.c	$2$	$2$	$2$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			525.2.b.c	$4$	$0$	$0$	$0$	$0$	$5$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1-2\zeta_{6})q^{3}+2q^{4}+(3-\zeta_{6})q^{7}+\cdots$
525.2.b.e	$525$	$2$	525.b	21.c	$2$	$4$	$4$	$4.192$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					105.2.b.c	$2$	$0$	$0$	$-1$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
525.2.b.f	$525$	$2$	525.b	21.c	$2$	$4$	$4$	$4.192$	$\Q(\sqrt{5}, \sqrt{-7})$	$_{}$	$\Q(\sqrt{-35}) $	None					105.2.g.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{3}+2q^{4}+(\beta _{1}-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$
525.2.b.g	$525$	$2$	525.b	21.c	$2$	$4$	$4$	$4.192$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					105.2.b.c	$2$	$0$	$0$	$1$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
525.2.b.h	$525$	$2$	525.b	21.c	$2$	$8$	$8$	$4.192$	8.0.$\cdots$.7	$_{}$	None	None		✓			525.2.b.h	$4$	$0$	$0$	$0$	$0$	$-8$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-2+\beta _{4})q^{4}+\beta _{3}q^{6}+\cdots$
525.2.b.i	$525$	$2$	525.b	21.c	$2$	$8$	$8$	$4.192$	8.0.$\cdots$.7	$_{}$	None	None		✓			525.2.b.h	$4$	$0$	$0$	$0$	$0$	$8$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-2+\beta _{4})q^{4}-\beta _{5}q^{6}+\cdots$
525.2.b.j	$525$	$2$	525.b	21.c	$2$	$8$	$8$	$4.192$	$\Q(\zeta_{24})$	$_{}$	None	None					105.2.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{2}-\beta_{3} q^{3}-q^{4}+(\beta_{4}+\beta_{2})q^{6}+\cdots$
525.2.d.a	$525$	$2$	525.d	5.b	$2$	$2$	$2$	$4.192$	$\Q(\sqrt{-1}) $	$_{}$	None	None					21.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}+q^{4}-q^{6}+i q^{7}+\cdots$
525.2.d.b	$525$	$2$	525.d	5.b	$2$	$2$	$2$	$4.192$	$\Q(\sqrt{-1}) $	$_{}$	None	None					105.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}+q^{4}+q^{6}+i q^{7}+\cdots$
525.2.d.c	$525$	$2$	525.d	5.b	$2$	$4$	$4$	$4.192$	$\Q(i, \sqrt{5})$	$_{}$	None	None					105.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}-3q^{4}+\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots$
525.2.d.d	$525$	$2$	525.d	5.b	$2$	$4$	$4$	$4.192$	$\Q(i, \sqrt{13})$	$_{}$	None	None		✓			525.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots$
525.2.d.e	$525$	$2$	525.d	5.b	$2$	$4$	$4$	$4.192$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			525.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots$
525.2.g.a	$525$	$2$	525.g	105.g	$2$	$4$	$4$	$4.192$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			525.2.b.c	$8$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta_1 q^{3}-2 q^{4}+(-\beta_{2}+\beta_1)q^{7}+\cdots$
525.2.g.b	$525$	$2$	525.g	105.g	$2$	$4$	$4$	$4.192$	$\Q(\zeta_{12})$	$_{}$	None	None					105.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}-\beta_1 q^{3}+q^{4}-3 q^{6}+\cdots$
525.2.g.c	$525$	$2$	525.g	105.g	$2$	$4$	$4$	$4.192$	$\Q(\zeta_{12})$	$_{}$	None	None					105.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{2}-\beta_1 q^{3}+q^{4}+3 q^{6}+\cdots$
525.2.g.d	$525$	$2$	525.g	105.g	$2$	$8$	$8$	$4.192$	$\Q(i, \sqrt{3}, \sqrt{11})$	$_{}$	None	None					105.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{4}-\beta _{5})q^{2}-\beta _{1}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
525.2.g.e	$525$	$2$	525.g	105.g	$2$	$8$	$8$	$4.192$	$\Q(i, \sqrt{3}, \sqrt{11})$	$_{}$	None	None					105.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots$
525.2.g.f	$525$	$2$	525.g	105.g	$2$	$16$	$16$	$4.192$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		525.2.b.h	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}-\beta _{8}q^{6}+\cdots$
525.2.i.a	$525$	$2$	525.i	7.c	$3$	$2$	$1$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.i.b	$2$	$0$	$-2$	$1$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
525.2.i.b	$525$	$2$	525.i	7.c	$3$	$2$	$1$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			525.2.i.b	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
525.2.i.c	$525$	$2$	525.i	7.c	$3$	$2$	$1$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.i.a	$2$	$0$	$0$	$1$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(-2-\zeta_{6})q^{7}+\cdots$
525.2.i.d	$525$	$2$	525.i	7.c	$3$	$2$	$1$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			525.2.i.b	$2$	$0$	$1$	$1$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
525.2.i.e	$525$	$2$	525.i	7.c	$3$	$2$	$1$	$4.192$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.e.a	$2$	$0$	$2$	$1$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
525.2.i.f	$525$	$2$	525.i	7.c	$3$	$4$	$2$	$4.192$	$\Q(\zeta_{12})$	$_{}$	None	None					105.2.i.d	$2$	$0$	$-2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
525.2.i.g	$525$	$2$	525.i	7.c	$3$	$4$	$2$	$4.192$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					105.2.i.c	$2$	$0$	$0$	$-2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{3}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
525.2.i.h	$525$	$2$	525.i	7.c	$3$	$8$	$4$	$4.192$	8.0.$\cdots$.5	$_{}$	None	None					105.2.q.a	$2$	$0$	$-2$	$4$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}-\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$
525.2.i.i	$525$	$2$	525.i	7.c	$3$	$8$	$4$	$4.192$	8.0.$\cdots$.1	$_{}$	None	None		✓			525.2.i.i	$2$	$0$	$-1$	$4$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots$
525.2.i.j	$525$	$2$	525.i	7.c	$3$	$8$	$4$	$4.192$	8.0.$\cdots$.1	$_{}$	None	None		✓			525.2.i.i	$2$	$0$	$1$	$-4$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots$
525.2.i.k	$525$	$2$	525.i	7.c	$3$	$8$	$4$	$4.192$	8.0.$\cdots$.5	$_{}$	None	None					105.2.q.a	$2$	$0$	$2$	$-4$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{3}-\beta _{4})q^{2}-\beta _{4}q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
525.2.j.a	$525$	$2$	525.j	15.e	$4$	$16$	$8$	$4.192$	$\Q(i, \sqrt{2}, \sqrt{3}, \sqrt{11})$	$_{}$	None	None		✓			525.2.j.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{10}+\beta _{13}-\beta _{15})q^{2}+\beta _{7}q^{3}+\cdots$
525.2.j.b	$525$	$2$	525.j	15.e	$4$	$24$	$12$	$4.192$		$_{}$	None	None					105.2.j.a	$4$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.