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 165 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
702.2.a.a	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.a	$1$	$0$	$-1$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots$
702.2.a.b	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.b	$1$	$1$	$-1$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots$
702.2.a.c	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.c	$1$	$0$	$-1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots$
702.2.a.d	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓	✓	✓	702.2.a.d	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+q^{13}+\cdots$
702.2.a.e	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.e	$1$	$1$	$-1$	$0$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-5q^{7}-q^{8}-q^{10}+\cdots$
702.2.a.f	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.f	$1$	$0$	$-1$	$0$	$2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-5q^{7}-q^{8}-2q^{10}+\cdots$
702.2.a.g	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.g	$1$	$0$	$-1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+4q^{7}-q^{8}-2q^{10}+\cdots$
702.2.a.h	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.h	$1$	$0$	$-1$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}+q^{7}-q^{8}-4q^{10}+\cdots$
702.2.a.i	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.h	$1$	$1$	$1$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots$
702.2.a.j	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓	✓	✓	702.2.a.f	$1$	$1$	$1$	$0$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-5q^{7}+q^{8}-2q^{10}+\cdots$
702.2.a.k	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.g	$1$	$0$	$1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+4q^{7}+q^{8}-2q^{10}+\cdots$
702.2.a.l	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.e	$1$	$1$	$1$	$0$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-5q^{7}+q^{8}-q^{10}+\cdots$
702.2.a.m	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.d	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+q^{13}+\cdots$
702.2.a.n	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.b	$1$	$0$	$1$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots$
702.2.a.o	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.c	$1$	$0$	$1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\cdots$
702.2.a.p	$702$	$2$	702.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	None	✓	✓			702.2.a.a	$1$	$0$	$1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots$
702.2.b.a	$702$	$2$	702.b	13.b	$2$	$2$	$2$	$5.605$	$\Q(\sqrt{-1}) $	None		✓			702.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+3 i q^{7}-i q^{8}+3 i q^{11}+\cdots$
702.2.b.b	$702$	$2$	702.b	13.b	$2$	$2$	$2$	$5.605$	$\Q(\sqrt{-1}) $	None		✓			702.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-i q^{8}-6 i q^{11}+(-3 i+2)q^{13}+\cdots$
702.2.b.c	$702$	$2$	702.b	13.b	$2$	$2$	$2$	$5.605$	$\Q(\sqrt{-1}) $	None		✓			702.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-i q^{8}-6 i q^{11}+(3 i+2)q^{13}+\cdots$
702.2.b.d	$702$	$2$	702.b	13.b	$2$	$2$	$2$	$5.605$	$\Q(\sqrt{-1}) $	None		✓			702.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-3 i q^{7}-i q^{8}+3 i q^{11}+\cdots$
702.2.b.e	$702$	$2$	702.b	13.b	$2$	$4$	$4$	$5.605$	$\Q(i, \sqrt{13})$	None		✓			702.2.b.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-2\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{8}+\cdots$
702.2.b.f	$702$	$2$	702.b	13.b	$2$	$4$	$4$	$5.605$	$\Q(i, \sqrt{10})$	None		✓			702.2.b.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
702.2.b.g	$702$	$2$	702.b	13.b	$2$	$4$	$4$	$5.605$	$\Q(i, \sqrt{10})$	None		✓			702.2.b.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
702.2.e.a	$702$	$2$	702.e	9.c	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None					234.2.e.a	$2$	$0$	$1$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
702.2.e.b	$702$	$2$	702.e	9.c	$3$	$4$	$2$	$5.605$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					234.2.e.c	$2$	$0$	$-2$	$0$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+\beta _{2}q^{5}+(-2+\cdots)q^{7}+\cdots$
702.2.e.c	$702$	$2$	702.e	9.c	$3$	$4$	$2$	$5.605$	$\Q(\zeta_{12})$	None					234.2.e.b	$2$	$0$	$-2$	$0$	$2$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_1-1)q^{2}-\beta_1 q^{4}+(-\beta_{2}+\beta_1)q^{5}+\cdots$
702.2.e.d	$702$	$2$	702.e	9.c	$3$	$6$	$3$	$5.605$	6.0.309123.1	None					234.2.e.d	$2$	$0$	$-3$	$0$	$-2$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+(-\beta _{2}+\beta _{5})q^{5}+\cdots$
702.2.e.e	$702$	$2$	702.e	9.c	$3$	$8$	$4$	$5.605$	8.0.508277025.1	None			✓		234.2.e.e	$2$	$0$	$4$	$0$	$2$	$-4$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}+\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots$
702.2.f.a	$702$	$2$	702.f	117.h	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None					234.2.f.b	$2$	$0$	$-2$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{4}+(1-\zeta_{6})q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
702.2.f.b	$702$	$2$	702.f	117.h	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None					234.2.f.a	$2$	$0$	$2$	$0$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(1-\zeta_{6})q^{7}+\cdots$
702.2.f.c	$702$	$2$	702.f	117.h	$3$	$12$	$6$	$5.605$	12.0.$\cdots$.1	None					234.2.f.d	$2$	$0$	$-12$	$0$	$-1$	$-5$		$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{4}+(-\beta _{5}+\beta _{10})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
702.2.f.d	$702$	$2$	702.f	117.h	$3$	$12$	$6$	$5.605$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					234.2.f.c	$2$	$0$	$12$	$0$	$3$	$1$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+q^{4}+(1+\beta _{1}+\beta _{8})q^{5}-\beta _{2}q^{7}+\cdots$
702.2.g.a	$702$	$2$	702.g	117.f	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None					234.2.f.a	$2$	$1$	$-1$	$0$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots$
702.2.g.b	$702$	$2$	702.g	117.f	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None					234.2.f.b	$2$	$0$	$1$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+q^{7}+\cdots$
702.2.g.c	$702$	$2$	702.g	117.f	$3$	$12$	$6$	$5.605$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					234.2.f.c	$2$	$0$	$-6$	$0$	$3$	$-2$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{8}q^{2}+(-1-\beta _{8})q^{4}+\beta _{5}q^{5}+\beta _{11}q^{7}+\cdots$
702.2.g.d	$702$	$2$	702.g	117.f	$3$	$12$	$6$	$5.605$	12.0.$\cdots$.1	None					234.2.f.d	$2$	$0$	$6$	$0$	$-1$	$10$		$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{5}+\beta _{10}+\cdots)q^{5}+\cdots$
702.2.h.a	$702$	$2$	702.h	13.c	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None		✓			702.2.h.a	$2$	$1$	$-1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{7}+\cdots$
702.2.h.b	$702$	$2$	702.h	13.c	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None		✓			702.2.h.b	$2$	$0$	$-1$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}-4\zeta_{6}q^{7}+\cdots$
702.2.h.c	$702$	$2$	702.h	13.c	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None		✓			702.2.h.c	$2$	$0$	$-1$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}+2\zeta_{6}q^{7}+\cdots$
702.2.h.d	$702$	$2$	702.h	13.c	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None		✓			702.2.h.b	$2$	$1$	$1$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2q^{5}-4\zeta_{6}q^{7}+\cdots$
702.2.h.e	$702$	$2$	702.h	13.c	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None		✓			702.2.h.c	$2$	$0$	$1$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2q^{5}+2\zeta_{6}q^{7}+\cdots$
702.2.h.f	$702$	$2$	702.h	13.c	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	None		✓			702.2.h.a	$2$	$0$	$1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{7}-q^{8}+\cdots$
702.2.h.g	$702$	$2$	702.h	13.c	$3$	$4$	$2$	$5.605$	$\Q(\sqrt{-3}, \sqrt{13})$	None		✓			702.2.h.g	$2$	$0$	$-2$	$0$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots$
702.2.h.h	$702$	$2$	702.h	13.c	$3$	$4$	$2$	$5.605$	$\Q(\sqrt{-3}, \sqrt{10})$	None		✓			702.2.h.h	$2$	$0$	$-2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+\beta _{3}q^{5}+(2+\cdots)q^{7}+\cdots$
702.2.h.i	$702$	$2$	702.h	13.c	$3$	$4$	$2$	$5.605$	$\Q(\sqrt{-3}, \sqrt{37})$	None		✓			702.2.h.i	$2$	$0$	$-2$	$0$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{2}-\beta _{2}q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
702.2.h.j	$702$	$2$	702.h	13.c	$3$	$4$	$2$	$5.605$	$\Q(\sqrt{-3}, \sqrt{37})$	None		✓			702.2.h.i	$2$	$0$	$2$	$0$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{2}-\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+\cdots$
702.2.h.k	$702$	$2$	702.h	13.c	$3$	$4$	$2$	$5.605$	$\Q(\sqrt{-3}, \sqrt{10})$	None		✓			702.2.h.h	$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{3}q^{5}-2\beta _{2}q^{7}+\cdots$
702.2.h.l	$702$	$2$	702.h	13.c	$3$	$4$	$2$	$5.605$	$\Q(\sqrt{-3}, \sqrt{13})$	None		✓			702.2.h.g	$2$	$0$	$2$	$0$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(1-\beta _{3})q^{5}+\cdots$
702.2.j.a	$702$	$2$	702.j	39.f	$4$	$16$	$8$	$5.605$	16.0.$\cdots$.9	None		✓			702.2.j.a	$4$	$0$	$0$	$0$	$0$	$8$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{12}q^{2}-\beta _{10}q^{4}+(-\beta _{2}-\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots$
702.2.j.b	$702$	$2$	702.j	39.f	$4$	$24$	$12$	$5.605$		None		✓	✓		702.2.j.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.