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 247 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
546.2.a.a	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	$\Q$	None	✓	✓	✓	✓	546.2.a.a	$1$	$0$	$-1$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
546.2.a.b	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	$\Q$	None	✓	✓	✓	✓	546.2.a.b	$1$	$1$	$-1$	$1$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
546.2.a.c	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	$\Q$	None	✓	✓	✓	✓	546.2.a.c	$1$	$0$	$-1$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
546.2.a.d	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	$\Q$	None	✓	✓	✓	✓	546.2.a.d	$1$	$0$	$-1$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots$
546.2.a.e	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	$\Q$	None	✓	✓	✓	✓	546.2.a.e	$1$	$0$	$1$	$-1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots$
546.2.a.f	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	$\Q$	None	✓	✓			546.2.a.f	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
546.2.a.g	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	$\Q$	None	✓	✓			546.2.a.g	$1$	$0$	$1$	$1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
546.2.a.h	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	$\Q(\sqrt{57}) $	None	✓	✓	✓	✓	546.2.a.h	$1$	$0$	$-2$	$-2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}+q^{7}+\cdots$
546.2.a.i	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	$\Q(\sqrt{41}) $	None	✓	✓	✓	✓	546.2.a.i	$1$	$0$	$2$	$-2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots$
546.2.a.j	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	546.2.a.j	$1$	$0$	$2$	$2$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(2-\beta )q^{5}+q^{6}+\cdots$
546.2.c.a	$546$	$2$	546.c	13.b	$2$	$2$	$2$	$4.360$	$\Q(\sqrt{-1}) $	None		✓			546.2.c.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{3}-q^{4}-i q^{5}-i q^{6}+\cdots$
546.2.c.b	$546$	$2$	546.c	13.b	$2$	$2$	$2$	$4.360$	$\Q(\sqrt{-1}) $	None		✓			546.2.c.b	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{3}-q^{4}+2 i q^{5}+i q^{6}+\cdots$
546.2.c.c	$546$	$2$	546.c	13.b	$2$	$2$	$2$	$4.360$	$\Q(\sqrt{-1}) $	None		✓			546.2.c.c	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{3}-q^{4}-i q^{5}+i q^{6}+\cdots$
546.2.c.d	$546$	$2$	546.c	13.b	$2$	$2$	$2$	$4.360$	$\Q(\sqrt{-1}) $	None		✓			546.2.c.d	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{3}-q^{4}-3 i q^{5}+i q^{6}+\cdots$
546.2.c.e	$546$	$2$	546.c	13.b	$2$	$4$	$4$	$4.360$	$\Q(i, \sqrt{17})$	None		✓	✓		546.2.c.e	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{3}-q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
546.2.e.a	$546$	$2$	546.e	273.g	$2$	$2$	$2$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.e.a	$2$	$0$	$-2$	$-3$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+2\zeta_{6})q^{5}+\cdots$
546.2.e.b	$546$	$2$	546.e	273.g	$2$	$2$	$2$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.e.a	$2$	$0$	$-2$	$3$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{5}+\cdots$
546.2.e.c	$546$	$2$	546.e	273.g	$2$	$2$	$2$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.e.a	$2$	$0$	$2$	$-3$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{5}+\cdots$
546.2.e.d	$546$	$2$	546.e	273.g	$2$	$2$	$2$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.e.a	$2$	$0$	$2$	$3$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+2\zeta_{6})q^{5}+\cdots$
546.2.e.e	$546$	$2$	546.e	273.g	$2$	$8$	$8$	$4.360$	$\Q(i, \sqrt{3}, \sqrt{11})$	None		✓			546.2.e.e	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{5}+\beta _{7})q^{5}+\cdots$
546.2.e.f	$546$	$2$	546.e	273.g	$2$	$8$	$8$	$4.360$	8.0.$\cdots$.11	None		✓			546.2.e.f	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots$
546.2.e.g	$546$	$2$	546.e	273.g	$2$	$8$	$8$	$4.360$	$\Q(i, \sqrt{3}, \sqrt{11})$	None		✓			546.2.e.e	$4$	$0$	$8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{5}-\beta _{7})q^{5}+\cdots$
546.2.e.h	$546$	$2$	546.e	273.g	$2$	$8$	$8$	$4.360$	8.0.$\cdots$.11	None		✓			546.2.e.f	$4$	$0$	$8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots$
546.2.g.a	$546$	$2$	546.g	21.c	$2$	$4$	$4$	$4.360$	$\Q(i, \sqrt{5})$	None		✓			546.2.g.a	$2$	$0$	$0$	$-2$	$4$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
546.2.g.b	$546$	$2$	546.g	21.c	$2$	$4$	$4$	$4.360$	$\Q(i, \sqrt{5})$	None		✓			546.2.g.a	$2$	$0$	$0$	$2$	$-4$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots$
546.2.g.c	$546$	$2$	546.g	21.c	$2$	$12$	$12$	$4.360$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			546.2.g.c	$2$	$0$	$0$	$-2$	$4$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{4}q^{5}+\beta _{6}q^{6}+\cdots$
546.2.g.d	$546$	$2$	546.g	21.c	$2$	$12$	$12$	$4.360$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			546.2.g.c	$2$	$0$	$0$	$2$	$-4$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{4}q^{5}-\beta _{6}q^{6}+\cdots$
546.2.i.a	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.i.a	$2$	$1$	$-1$	$-1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
546.2.i.b	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.i.b	$2$	$0$	$-1$	$-1$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
546.2.i.c	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.i.c	$2$	$0$	$-1$	$-1$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
546.2.i.d	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.i.d	$2$	$0$	$-1$	$1$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
546.2.i.e	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.i.e	$2$	$0$	$1$	$-1$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
546.2.i.f	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.i.f	$2$	$0$	$1$	$1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
546.2.i.g	$546$	$2$	546.i	7.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.i.g	$2$	$0$	$1$	$1$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
546.2.i.h	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			546.2.i.h	$2$	$0$	$-2$	$-2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots$
546.2.i.i	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			546.2.i.i	$2$	$0$	$-2$	$2$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots$
546.2.i.j	$546$	$2$	546.i	7.c	$3$	$4$	$2$	$4.360$	$\Q(\sqrt{-3}, \sqrt{7})$	None		✓			546.2.i.j	$2$	$0$	$2$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
546.2.i.k	$546$	$2$	546.i	7.c	$3$	$6$	$3$	$4.360$	6.0.21870000.1	None		✓	✓		546.2.i.k	$2$	$0$	$3$	$3$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
546.2.j.a	$546$	$2$	546.j	91.h	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.j.a	$2$	$0$	$2$	$1$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}+(2-3\zeta_{6})q^{7}+\cdots$
546.2.j.b	$546$	$2$	546.j	91.h	$3$	$8$	$4$	$4.360$	8.0.6498455769.2	None		✓			546.2.j.b	$2$	$0$	$-8$	$-4$	$-2$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots$
546.2.j.c	$546$	$2$	546.j	91.h	$3$	$8$	$4$	$4.360$	8.0.447703281.1	None		✓			546.2.j.c	$2$	$0$	$8$	$-4$	$2$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
546.2.j.d	$546$	$2$	546.j	91.h	$3$	$8$	$4$	$4.360$	8.0.447703281.1	None		✓			546.2.j.d	$2$	$0$	$8$	$4$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-\beta _{3}q^{3}+q^{4}+(2\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
546.2.j.e	$546$	$2$	546.j	91.h	$3$	$10$	$5$	$4.360$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓		546.2.j.e	$2$	$0$	$-10$	$5$	$-2$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1+\beta _{5})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots$
546.2.k.a	$546$	$2$	546.k	91.g	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.j.a	$2$	$0$	$-1$	$-2$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}-q^{3}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{6}+\cdots$
546.2.k.b	$546$	$2$	546.k	91.g	$3$	$8$	$4$	$4.360$	8.0.447703281.1	None		✓			546.2.j.d	$2$	$0$	$-4$	$-8$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}-q^{3}+(-1-\beta _{3})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots$
546.2.k.c	$546$	$2$	546.k	91.g	$3$	$8$	$4$	$4.360$	8.0.447703281.1	None		✓			546.2.j.c	$2$	$0$	$-4$	$8$	$2$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
546.2.k.d	$546$	$2$	546.k	91.g	$3$	$8$	$4$	$4.360$	8.0.6498455769.2	None		✓			546.2.j.b	$2$	$0$	$4$	$8$	$-2$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}+q^{3}-\beta _{4}q^{4}+\beta _{2}q^{5}+\cdots$
546.2.k.e	$546$	$2$	546.k	91.g	$3$	$10$	$5$	$4.360$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓		546.2.j.e	$2$	$0$	$5$	$-10$	$-2$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{5})q^{2}-q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
546.2.l.a	$546$	$2$	546.l	13.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.l.a	$2$	$1$	$-1$	$-1$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
546.2.l.b	$546$	$2$	546.l	13.c	$3$	$2$	$1$	$4.360$	$\Q(\sqrt{-3}) $	None		✓			546.2.l.b	$2$	$0$	$-1$	$1$	$6$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$

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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.