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 89 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
2106.2.a.a	$2106$	$2$	2106.a	1.a	$1$	$1$	$1$	$16.816$	$\Q$	None	✓	✓			2106.2.a.a	$1$	$0$	$-1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
2106.2.a.b	$2106$	$2$	2106.a	1.a	$1$	$1$	$1$	$16.816$	$\Q$	None	✓				234.2.e.a	$1$	$1$	$-1$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots$
2106.2.a.c	$2106$	$2$	2106.a	1.a	$1$	$1$	$1$	$16.816$	$\Q$	None	✓	✓			2106.2.a.c	$1$	$0$	$-1$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots$
2106.2.a.d	$2106$	$2$	2106.a	1.a	$1$	$1$	$1$	$16.816$	$\Q$	None	✓				234.2.e.a	$1$	$1$	$1$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-2q^{7}+q^{8}-2q^{10}+\cdots$
2106.2.a.e	$2106$	$2$	2106.a	1.a	$1$	$1$	$1$	$16.816$	$\Q$	None	✓	✓			2106.2.a.c	$1$	$1$	$1$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots$
2106.2.a.f	$2106$	$2$	2106.a	1.a	$1$	$1$	$1$	$16.816$	$\Q$	None	✓	✓			2106.2.a.a	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots$
2106.2.a.g	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{6}) $	None	✓	✓			2106.2.a.g	$1$	$1$	$-2$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{5}+q^{7}-q^{8}+\cdots$
2106.2.a.h	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{6}) $	None	✓				234.2.e.c	$1$	$0$	$-2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots$
2106.2.a.i	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{3}) $	None	✓				234.2.e.b	$1$	$1$	$-2$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}-2q^{7}-q^{8}+\cdots$
2106.2.a.j	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{3}) $	None	✓	✓			2106.2.a.j	$1$	$0$	$-2$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}+(-2+\beta )q^{7}+\cdots$
2106.2.a.k	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{3}) $	None	✓	✓			2106.2.a.k	$1$	$1$	$-2$	$0$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}+(1-2\beta )q^{7}+\cdots$
2106.2.a.l	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{3}) $	None	✓	✓			2106.2.a.j	$1$	$1$	$2$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{5}+(-2-\beta )q^{7}+\cdots$
2106.2.a.m	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{3}) $	None	✓				234.2.e.b	$1$	$1$	$2$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{5}-2q^{7}+q^{8}+\cdots$
2106.2.a.n	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{3}) $	None	✓	✓			2106.2.a.k	$1$	$0$	$2$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{5}+(1+2\beta )q^{7}+\cdots$
2106.2.a.o	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{6}) $	None	✓				234.2.e.c	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots$
2106.2.a.p	$2106$	$2$	2106.a	1.a	$1$	$2$	$2$	$16.816$	$\Q(\sqrt{6}) $	None	✓	✓			2106.2.a.g	$1$	$0$	$2$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta )q^{5}+q^{7}+q^{8}+\cdots$
2106.2.a.q	$2106$	$2$	2106.a	1.a	$1$	$3$	$3$	$16.816$	3.3.321.1	None	✓		✓		234.2.e.d	$1$	$0$	$-3$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
2106.2.a.r	$2106$	$2$	2106.a	1.a	$1$	$3$	$3$	$16.816$	3.3.321.1	None	✓				234.2.e.d	$1$	$0$	$3$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
2106.2.a.s	$2106$	$2$	2106.a	1.a	$1$	$4$	$4$	$16.816$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	✓	✓		2106.2.a.s	$1$	$1$	$-4$	$0$	$-2$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
2106.2.a.t	$2106$	$2$	2106.a	1.a	$1$	$4$	$4$	$16.816$	4.4.22545.1	None	✓		✓		234.2.e.e	$1$	$0$	$-4$	$0$	$-2$	$4$	$-$	$3$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}-q^{8}+\cdots$
2106.2.a.u	$2106$	$2$	2106.a	1.a	$1$	$4$	$4$	$16.816$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	✓	✓		2106.2.a.s	$1$	$0$	$4$	$0$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
2106.2.a.v	$2106$	$2$	2106.a	1.a	$1$	$4$	$4$	$16.816$	4.4.22545.1	None	✓		✓		234.2.e.e	$1$	$0$	$4$	$0$	$2$	$4$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{3})q^{7}+q^{8}+\cdots$
2106.2.b.a	$2106$	$2$	2106.b	13.b	$2$	$6$	$6$	$16.816$	6.0.5089536.1	None		✓			2106.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-q^{4}+(\beta _{4}+\beta _{5})q^{5}+\beta _{2}q^{7}+\cdots$
2106.2.b.b	$2106$	$2$	2106.b	13.b	$2$	$6$	$6$	$16.816$	6.0.5089536.1	None		✓			2106.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-q^{4}+(\beta _{4}+\beta _{5})q^{5}-\beta _{2}q^{7}+\cdots$
2106.2.b.c	$2106$	$2$	2106.b	13.b	$2$	$14$	$14$	$16.816$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None					234.2.t.a	$2$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-q^{4}-\beta _{11}q^{5}+(\beta _{1}+\beta _{8}+\cdots)q^{7}+\cdots$
2106.2.b.d	$2106$	$2$	2106.b	13.b	$2$	$14$	$14$	$16.816$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None					234.2.t.a	$2$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-q^{4}-\beta _{11}q^{5}+(-\beta _{1}-\beta _{8}+\cdots)q^{7}+\cdots$
2106.2.b.e	$2106$	$2$	2106.b	13.b	$2$	$16$	$16$	$16.816$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		2106.2.b.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}-q^{4}-\beta _{1}q^{5}+(-\beta _{5}-\beta _{9}+\cdots)q^{7}+\cdots$
2106.2.e.a	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.a	$2$	$0$	$-1$	$0$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$
2106.2.e.b	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					26.2.a.a	$2$	$0$	$-1$	$0$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$
2106.2.e.c	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.c	$2$	$0$	$-1$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
2106.2.e.d	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.b	$2$	$1$	$-1$	$0$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
2106.2.e.e	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					234.2.a.a	$2$	$0$	$-1$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
2106.2.e.f	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.d	$2$	$0$	$-1$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots$
2106.2.e.g	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None		✓			2106.2.a.a	$2$	$1$	$-1$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots$
2106.2.e.h	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					26.2.a.b	$2$	$0$	$-1$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$
2106.2.e.i	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.e	$2$	$0$	$-1$	$0$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots$
2106.2.e.j	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					78.2.a.a	$2$	$0$	$-1$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
2106.2.e.k	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.g	$2$	$0$	$-1$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
2106.2.e.l	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None		✓			2106.2.a.c	$2$	$0$	$-1$	$0$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
2106.2.e.m	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.f	$2$	$0$	$-1$	$0$	$2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
2106.2.e.n	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.h	$2$	$0$	$-1$	$0$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+\cdots$
2106.2.e.o	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.h	$2$	$0$	$1$	$0$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$
2106.2.e.p	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.g	$2$	$0$	$1$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots$
2106.2.e.q	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					78.2.a.a	$2$	$0$	$1$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots$
2106.2.e.r	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None		✓			2106.2.a.c	$2$	$0$	$1$	$0$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$
2106.2.e.s	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.f	$2$	$0$	$1$	$0$	$-2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots$
2106.2.e.t	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					26.2.a.b	$2$	$0$	$1$	$0$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$
2106.2.e.u	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.e	$2$	$0$	$1$	$0$	$-1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(5-5\zeta_{6})q^{7}+\cdots$
2106.2.e.v	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None		✓			2106.2.a.a	$2$	$0$	$1$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots$
2106.2.e.w	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	$\Q(\sqrt{-3}) $	None					702.2.a.d	$2$	$0$	$1$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots$

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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.