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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 205 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
245.2.a.a	$245$	$2$	245.a	1.a	$1$	$1$	$1$	$1.956$	$\Q$	None	✓	✓			245.2.a.a	$1$	$1$	$-2$	$-3$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots$
245.2.a.b	$245$	$2$	245.a	1.a	$1$	$1$	$1$	$1.956$	$\Q$	None	✓	✓			245.2.a.a	$1$	$0$	$-2$	$3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+2q^{4}-q^{5}-6q^{6}+\cdots$
245.2.a.c	$245$	$2$	245.a	1.a	$1$	$1$	$1$	$1.956$	$\Q$	None	✓				35.2.a.a	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}-2q^{9}-3q^{11}+\cdots$
245.2.a.d	$245$	$2$	245.a	1.a	$1$	$2$	$2$	$1.956$	$\Q(\sqrt{17}) $	None	✓				35.2.a.b	$1$	$0$	$-1$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1-\beta )q^{3}+(2+\beta )q^{4}-q^{5}+\cdots$
245.2.a.e	$245$	$2$	245.a	1.a	$1$	$2$	$2$	$1.956$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	245.2.a.e	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1-\beta )q^{3}-q^{5}+(-2-\beta )q^{6}+\cdots$
245.2.a.f	$245$	$2$	245.a	1.a	$1$	$2$	$2$	$1.956$	$\Q(\sqrt{2}) $	None	✓	✓			245.2.a.e	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+q^{5}+(2+\beta )q^{6}+\cdots$
245.2.a.g	$245$	$2$	245.a	1.a	$1$	$2$	$2$	$1.956$	$\Q(\sqrt{2}) $	None	✓				35.2.e.a	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1+\beta )q^{3}+(1+2\beta )q^{4}+\cdots$
245.2.a.h	$245$	$2$	245.a	1.a	$1$	$2$	$2$	$1.956$	$\Q(\sqrt{2}) $	None	✓				35.2.e.a	$1$	$0$	$2$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots$
245.2.b.a	$245$	$2$	245.b	5.b	$2$	$2$	$2$	$1.956$	$\Q(\sqrt{-1}) $	None					35.2.b.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}+i q^{3}-2 q^{4}+(i+2)q^{5}+\cdots$
245.2.b.b	$245$	$2$	245.b	5.b	$2$	$2$	$2$	$1.956$	$\Q(\sqrt{-1}) $	None					35.2.j.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}+q^{4}+(2 i-1)q^{5}+\cdots$
245.2.b.c	$245$	$2$	245.b	5.b	$2$	$2$	$2$	$1.956$	$\Q(\sqrt{-1}) $	None					35.2.j.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}+q^{4}+(-2 i+1)q^{5}+\cdots$
245.2.b.d	$245$	$2$	245.b	5.b	$2$	$2$	$2$	$1.956$	$\Q(\sqrt{-5}) $	$\Q(\sqrt{-35}) $		✓			245.2.b.d	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}+2q^{4}+\beta q^{5}-2q^{9}-3q^{11}+\cdots$
245.2.b.e	$245$	$2$	245.b	5.b	$2$	$4$	$4$	$1.956$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			245.2.b.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{2}q^{3}-4q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
245.2.b.f	$245$	$2$	245.b	5.b	$2$	$4$	$4$	$1.956$	$\Q(\zeta_{8})$	None		✓			245.2.b.f	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(2\zeta_{8}+2\zeta_{8}^{3})q^{3}+q^{4}+\cdots$
245.2.e.a	$245$	$2$	245.e	7.c	$3$	$2$	$1$	$1.956$	$\Q(\sqrt{-3}) $	None					35.2.a.a	$2$	$0$	$0$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$
245.2.e.b	$245$	$2$	245.e	7.c	$3$	$2$	$1$	$1.956$	$\Q(\sqrt{-3}) $	None					35.2.a.a	$2$	$0$	$0$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$
245.2.e.c	$245$	$2$	245.e	7.c	$3$	$2$	$1$	$1.956$	$\Q(\sqrt{-3}) $	None		✓			245.2.a.a	$2$	$0$	$2$	$-3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
245.2.e.d	$245$	$2$	245.e	7.c	$3$	$2$	$1$	$1.956$	$\Q(\sqrt{-3}) $	None		✓			245.2.a.a	$2$	$0$	$2$	$3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
245.2.e.e	$245$	$2$	245.e	7.c	$3$	$4$	$2$	$1.956$	$\Q(\sqrt{2}, \sqrt{-3})$	None					35.2.e.a	$2$	$0$	$-2$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
245.2.e.f	$245$	$2$	245.e	7.c	$3$	$4$	$2$	$1.956$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			245.2.a.e	$2$	$0$	$0$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1+\cdots)q^{5}+\cdots$
245.2.e.g	$245$	$2$	245.e	7.c	$3$	$4$	$2$	$1.956$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			245.2.a.e	$2$	$0$	$0$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
245.2.e.h	$245$	$2$	245.e	7.c	$3$	$4$	$2$	$1.956$	$\Q(\sqrt{-3}, \sqrt{17})$	None					35.2.a.b	$2$	$0$	$1$	$-1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$
245.2.e.i	$245$	$2$	245.e	7.c	$3$	$4$	$2$	$1.956$	$\Q(\sqrt{-3}, \sqrt{17})$	None					35.2.a.b	$2$	$0$	$1$	$1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots$
245.2.f.a	$245$	$2$	245.f	35.f	$4$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	None					35.2.k.a	$2$	$0$	$2$	$-2$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{2}-\beta_1+1)q^{2}+(-\beta_{2}+\beta_1-1)q^{3}+\cdots$
245.2.f.b	$245$	$2$	245.f	35.f	$4$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	None					35.2.k.a	$2$	$0$	$2$	$2$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{2}-\beta_1+1)q^{2}+(\beta_{2}-\beta_1+1)q^{3}+\cdots$
245.2.f.c	$245$	$2$	245.f	35.f	$4$	$24$	$12$	$1.956$		None		✓	✓		245.2.f.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
245.2.j.a	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			245.2.b.e	$4$	$0$	$0$	$-6$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(4+4\beta _{2}+\cdots)q^{4}+\cdots$
245.2.j.b	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	$\Q(\sqrt{-3}, \sqrt{-5})$	$\Q(\sqrt{-35}) $		✓			245.2.b.d	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{3}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
245.2.j.c	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	None					35.2.j.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
245.2.j.d	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	None					35.2.b.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots$
245.2.j.e	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	None					35.2.b.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots$
245.2.j.f	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			245.2.b.e	$4$	$0$	$0$	$6$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(4+4\beta _{2}+\cdots)q^{4}+\cdots$
245.2.j.g	$245$	$2$	245.j	35.j	$6$	$8$	$4$	$1.956$	$\Q(\zeta_{24})$	None		✓	✓		245.2.b.f	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(2\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{3}+\cdots$
245.2.k.a	$245$	$2$	245.k	49.e	$7$	$54$	$9$	$1.956$		None		✓			245.2.k.a	$2$	$0$	$1$	$-2$	$9$	$-1$			$\mathrm{SU}(2)[C_{7}]$
245.2.k.b	$245$	$2$	245.k	49.e	$7$	$66$	$11$	$1.956$		None		✓	✓		245.2.k.b	$2$	$0$	$-1$	$-2$	$-11$	$-5$			$\mathrm{SU}(2)[C_{7}]$
245.2.l.a	$245$	$2$	245.l	35.k	$12$	$4$	$1$	$1.956$	$\Q(\zeta_{12})$	None					35.2.k.a	$2$	$0$	$-4$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\zeta_{12})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$
245.2.l.b	$245$	$2$	245.l	35.k	$12$	$4$	$1$	$1.956$	$\Q(\zeta_{12})$	None					35.2.k.a	$2$	$0$	$2$	$4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots$
245.2.l.c	$245$	$2$	245.l	35.k	$12$	$8$	$2$	$1.956$	$\Q(i, \sqrt{3}, \sqrt{10})$	None					35.2.f.a	$8$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1-\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{5}+\cdots$
245.2.l.d	$245$	$2$	245.l	35.k	$12$	$48$	$12$	$1.956$		None		✓	✓		245.2.f.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
245.2.p.a	$245$	$2$	245.p	245.p	$14$	$12$	$2$	$1.956$	$\Q(\zeta_{28})$	None		✓			245.2.p.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q-\zeta_{28}^{9}q^{2}+(-2\zeta_{28}^{3}+\zeta_{28}^{5}-\zeta_{28}^{7}+\cdots)q^{3}+\cdots$
245.2.p.b	$245$	$2$	245.p	245.p	$14$	$144$	$24$	$1.956$		None		✓	✓		245.2.p.b	$4$	$0$	$0$	$0$	$-1$	$0$			$\mathrm{SU}(2)[C_{14}]$
245.2.q.a	$245$	$2$	245.q	49.g	$21$	$96$	$8$	$1.956$		None		✓			245.2.q.a	$2$	$0$	$-1$	$1$	$-8$	$0$			$\mathrm{SU}(2)[C_{21}]$
245.2.q.b	$245$	$2$	245.q	49.g	$21$	$120$	$10$	$1.956$		None		✓	✓		245.2.q.b	$2$	$0$	$1$	$1$	$10$	$-2$			$\mathrm{SU}(2)[C_{21}]$
245.2.s.a	$245$	$2$	245.s	245.s	$28$	$312$	$26$	$1.956$		None		✓	✓	✓	245.2.s.a	$4$	$0$	$-10$	$-14$	$-14$	$-18$			$\mathrm{SU}(2)[C_{28}]$
245.2.t.a	$245$	$2$	245.t	245.t	$42$	$312$	$26$	$1.956$		None		✓	✓	✓	245.2.t.a	$4$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{42}]$
245.2.x.a	$245$	$2$	245.x	245.x	$84$	$624$	$26$	$1.956$		None		✓	✓	✓	245.2.x.a	$4$	$0$	$-26$	$-22$	$-28$	$-18$			$\mathrm{SU}(2)[C_{84}]$
245.3.c.a	$245$	$3$	245.c	35.c	$2$	$12$	$12$	$6.676$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					35.3.i.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{9}q^{3}+(-1+\beta _{1})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots$
245.3.c.b	$245$	$3$	245.c	35.c	$2$	$24$	$24$	$6.676$		None		✓	✓		245.3.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
245.3.d.a	$245$	$3$	245.d	7.b	$2$	$12$	$12$	$6.676$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					35.3.h.a	$2$	$0$	$4$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{5}+\beta _{6})q^{4}+\cdots$
245.3.d.b	$245$	$3$	245.d	7.b	$2$	$16$	$16$	$6.676$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		245.3.d.b	$2$	$0$	$-8$	$0$	$0$	$0$		$2^{6}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+\beta _{6}q^{3}+(3-\beta _{1})q^{4}+\cdots$

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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.