LMFDB - Newform search results

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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 189 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
810.2.a.a	$810$	$2$	810.a	1.a	$1$	$1$	$1$	$6.468$	$\Q$	None	✓				90.2.e.b	$1$	$0$	$-1$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
810.2.a.b	$810$	$2$	810.a	1.a	$1$	$1$	$1$	$6.468$	$\Q$	None	✓		✓	✓	90.2.e.a	$1$	$1$	$-1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
810.2.a.c	$810$	$2$	810.a	1.a	$1$	$1$	$1$	$6.468$	$\Q$	None	✓	✓			810.2.a.c	$1$	$0$	$-1$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
810.2.a.d	$810$	$2$	810.a	1.a	$1$	$1$	$1$	$6.468$	$\Q$	None	✓	✓			810.2.a.d	$1$	$0$	$-1$	$0$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+5q^{7}-q^{8}-q^{10}+\cdots$
810.2.a.e	$810$	$2$	810.a	1.a	$1$	$1$	$1$	$6.468$	$\Q$	None	✓		✓	✓	90.2.e.b	$1$	$1$	$1$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
810.2.a.f	$810$	$2$	810.a	1.a	$1$	$1$	$1$	$6.468$	$\Q$	None	✓	✓			810.2.a.c	$1$	$0$	$1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
810.2.a.g	$810$	$2$	810.a	1.a	$1$	$1$	$1$	$6.468$	$\Q$	None	✓				90.2.e.a	$1$	$0$	$1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
810.2.a.h	$810$	$2$	810.a	1.a	$1$	$1$	$1$	$6.468$	$\Q$	None	✓	✓			810.2.a.d	$1$	$0$	$1$	$0$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+5q^{7}+q^{8}-q^{10}+\cdots$
810.2.a.i	$810$	$2$	810.a	1.a	$1$	$2$	$2$	$6.468$	$\Q(\sqrt{33}) $	None	✓		✓	✓	90.2.e.c	$1$	$1$	$-2$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots$
810.2.a.j	$810$	$2$	810.a	1.a	$1$	$2$	$2$	$6.468$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	810.2.a.j	$1$	$0$	$-2$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(2+\beta )q^{7}-q^{8}+\cdots$
810.2.a.k	$810$	$2$	810.a	1.a	$1$	$2$	$2$	$6.468$	$\Q(\sqrt{33}) $	None	✓				90.2.e.c	$1$	$0$	$2$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots$
810.2.a.l	$810$	$2$	810.a	1.a	$1$	$2$	$2$	$6.468$	$\Q(\sqrt{3}) $	None	✓	✓			810.2.a.j	$1$	$0$	$2$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(2+\beta )q^{7}+q^{8}+\cdots$
810.2.c.a	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	$\Q(\sqrt{-1}) $	None		✓			810.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(i-2)q^{5}+i q^{7}+\cdots$
810.2.c.b	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	$\Q(\sqrt{-1}) $	None					90.2.i.a	$2$	$1$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(2 i-1)q^{5}+i q^{7}+\cdots$
810.2.c.c	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	$\Q(\sqrt{-1}) $	None					90.2.i.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(-2 i+1)q^{5}+i q^{7}+\cdots$
810.2.c.d	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	$\Q(\sqrt{-1}) $	None		✓			810.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(-i+2)q^{5}+i q^{7}+\cdots$
810.2.c.e	$810$	$2$	810.c	5.b	$2$	$4$	$4$	$6.468$	$\Q(i, \sqrt{6})$	None					90.2.i.b	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$
810.2.c.f	$810$	$2$	810.c	5.b	$2$	$4$	$4$	$6.468$	$\Q(i, \sqrt{6})$	None					90.2.i.b	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
810.2.c.g	$810$	$2$	810.c	5.b	$2$	$8$	$8$	$6.468$	8.0.2702336256.1	None		✓	✓		810.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-q^{4}+\beta _{7}q^{5}-\beta _{3}q^{7}+\beta _{6}q^{8}+\cdots$
810.2.e.a	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None					270.2.a.a	$2$	$0$	$-1$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
810.2.e.b	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None					30.2.a.a	$2$	$0$	$-1$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$
810.2.e.c	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None		✓			810.2.a.d	$2$	$0$	$-1$	$0$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots$
810.2.e.d	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None					270.2.a.b	$2$	$0$	$-1$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
810.2.e.e	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None					90.2.a.a	$2$	$0$	$-1$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
810.2.e.f	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None		✓			810.2.a.c	$2$	$0$	$-1$	$0$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
810.2.e.g	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None		✓			810.2.a.d	$2$	$0$	$1$	$0$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots$
810.2.e.h	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None					90.2.a.a	$2$	$0$	$1$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
810.2.e.i	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None					270.2.a.b	$2$	$0$	$1$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
810.2.e.j	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None		✓			810.2.a.c	$2$	$0$	$1$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
810.2.e.k	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None					270.2.a.a	$2$	$0$	$1$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
810.2.e.l	$810$	$2$	810.e	9.c	$3$	$2$	$1$	$6.468$	$\Q(\sqrt{-3}) $	None					30.2.a.a	$2$	$0$	$1$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots$
810.2.e.m	$810$	$2$	810.e	9.c	$3$	$4$	$2$	$6.468$	$\Q(\zeta_{12})$	None		✓			810.2.a.j	$2$	$0$	$-2$	$0$	$-2$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_1 q^{2}+(\beta_1-1)q^{4}+(\beta_1-1)q^{5}+\cdots$
810.2.e.n	$810$	$2$	810.e	9.c	$3$	$4$	$2$	$6.468$	$\Q(\zeta_{12})$	None		✓			810.2.a.j	$2$	$0$	$2$	$0$	$2$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{2}+(\beta_1-1)q^{4}+(-\beta_1+1)q^{5}+\cdots$
810.2.f.a	$810$	$2$	810.f	15.e	$4$	$8$	$4$	$6.468$	$\Q(\zeta_{24})$	None		✓			810.2.f.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{3} q^{2}-\beta_{2} q^{4}+(-2\beta_{3}+\beta_1)q^{5}+\cdots$
810.2.f.b	$810$	$2$	810.f	15.e	$4$	$8$	$4$	$6.468$	$\Q(\zeta_{24})$	None					90.2.l.a	$4$	$0$	$0$	$0$	$0$	$16$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_1 q^{2}+\beta_{3} q^{4}+(\beta_{5}+\beta_{4}+\beta_1)q^{5}+\cdots$
810.2.f.c	$810$	$2$	810.f	15.e	$4$	$16$	$8$	$6.468$	16.0.$\cdots$.9	None					90.2.l.b	$4$	$0$	$0$	$0$	$0$	$-16$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{12}q^{2}+\beta _{13}q^{4}+(\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$
810.2.f.d	$810$	$2$	810.f	15.e	$4$	$16$	$8$	$6.468$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			810.2.f.d	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{14}q^{2}-\beta _{6}q^{4}+(-\beta _{9}+\beta _{13})q^{5}+\cdots$
810.2.i.a	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	$\Q(\zeta_{12})$	None		✓			810.2.c.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
810.2.i.b	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	$\Q(\zeta_{12})$	None					30.2.c.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
810.2.i.c	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	$\Q(\zeta_{12})$	None					270.2.c.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
810.2.i.d	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	$\Q(\zeta_{12})$	None					270.2.c.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
810.2.i.e	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	$\Q(\zeta_{12})$	None					30.2.c.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
810.2.i.f	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	$\Q(\zeta_{12})$	None		✓			810.2.c.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
810.2.i.g	$810$	$2$	810.i	45.j	$6$	$8$	$4$	$6.468$	8.0.2702336256.1	None		✓			810.2.c.g	$4$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{4}+\beta _{6})q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
810.2.i.h	$810$	$2$	810.i	45.j	$6$	$8$	$4$	$6.468$	8.0.2702336256.1	None					270.2.c.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}-\beta _{2}q^{4}-\beta _{1}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
810.2.i.i	$810$	$2$	810.i	45.j	$6$	$8$	$4$	$6.468$	8.0.2702336256.1	None		✓			810.2.c.g	$4$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{4}-\beta _{6})q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
810.2.k.a	$810$	$2$	810.k	27.e	$9$	$6$	$1$	$6.468$	$\Q(\zeta_{18})$	None					270.2.k.a	$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
810.2.k.b	$810$	$2$	810.k	27.e	$9$	$12$	$2$	$6.468$	12.0.$\cdots$.1	None					270.2.k.b	$2$	$0$	$0$	$0$	$0$	$-12$		$3^{3}$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{7}q^{2}+\beta _{9}q^{4}+(-\beta _{8}+\beta _{9})q^{5}+\cdots$
810.2.k.c	$810$	$2$	810.k	27.e	$9$	$12$	$2$	$6.468$	12.0.$\cdots$.1	None					270.2.k.c	$2$	$0$	$0$	$0$	$0$	$6$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{8}+\beta _{9})q^{2}+\beta _{7}q^{4}-\beta _{10}q^{5}+\cdots$
810.2.k.d	$810$	$2$	810.k	27.e	$9$	$18$	$3$	$6.468$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None					270.2.k.d	$2$	$0$	$0$	$0$	$0$	$-3$		$3^{5}$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{4}+(\beta _{2}+\beta _{4})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$

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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.