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 128 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
891.1.c.a	$891$	$1$	891.c	11.b	$2$	$1$	$1$	$0.445$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓				99.1.h.a	$2$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+q^{4}-q^{5}+q^{11}+q^{16}-q^{20}+2q^{23}+\cdots$
891.1.c.b	$891$	$1$	891.c	11.b	$2$	$1$	$1$	$0.445$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓				99.1.h.a	$2$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{4}+q^{5}-q^{11}+q^{16}+q^{20}-2q^{23}+\cdots$
891.1.q.a	$891$	$1$	891.q	297.q	$18$	$6$	$1$	$0.445$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None			✓	✓	297.1.q.a	$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}-\zeta_{18}^{4})q^{5}+\zeta_{18}q^{11}+\cdots$
891.1.w.a	$891$	$1$	891.w	891.w	$54$	$18$	$1$	$0.445$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	891.1.w.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{54}^{13}q^{3}+\zeta_{54}^{10}q^{4}+(\zeta_{54}^{6}+\zeta_{54}^{8}+\cdots)q^{5}+\cdots$
891.2.a.a	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	$\Q$	$_{}$	None	None	✓				99.2.e.c	$1$	$0$	$-2$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-2q^{5}+4q^{7}+4q^{10}+\cdots$
891.2.a.b	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	$\Q$	$_{}$	None	None	✓	✓			891.2.a.b	$1$	$1$	$-1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots$
891.2.a.c	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	$\Q$	$_{}$	None	None	✓				99.2.e.a	$1$	$0$	$-1$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots$
891.2.a.d	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	$\Q$	$_{}$	None	None	✓				99.2.e.b	$1$	$0$	$0$	$0$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{5}-4q^{7}+q^{11}+2q^{13}+\cdots$
891.2.a.e	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	$\Q$	$_{}$	None	None	✓				99.2.e.b	$1$	$0$	$0$	$0$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{5}-4q^{7}-q^{11}+2q^{13}+\cdots$
891.2.a.f	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	$\Q$	$_{}$	None	None	✓	✓			891.2.a.b	$1$	$0$	$1$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots$
891.2.a.g	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	$\Q$	$_{}$	None	None	✓				99.2.e.a	$1$	$0$	$1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots$
891.2.a.h	$891$	$2$	891.a	1.a	$1$	$1$	$1$	$7.115$	$\Q$	$_{}$	None	None	✓				99.2.e.c	$1$	$0$	$2$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+2q^{5}+4q^{7}+4q^{10}+\cdots$
891.2.a.i	$891$	$2$	891.a	1.a	$1$	$2$	$2$	$7.115$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			891.2.a.i	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots$
891.2.a.j	$891$	$2$	891.a	1.a	$1$	$2$	$2$	$7.115$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			891.2.a.i	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(-1+2\beta )q^{7}+\cdots$
891.2.a.k	$891$	$2$	891.a	1.a	$1$	$3$	$3$	$7.115$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				99.2.e.d	$1$	$1$	$0$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
891.2.a.l	$891$	$2$	891.a	1.a	$1$	$3$	$3$	$7.115$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				99.2.e.d	$1$	$1$	$0$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
891.2.a.m	$891$	$2$	891.a	1.a	$1$	$3$	$3$	$7.115$	3.3.837.1	$_{}$	None	None	✓	✓			891.2.a.m	$1$	$1$	$0$	$0$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{5}+\cdots$
891.2.a.n	$891$	$2$	891.a	1.a	$1$	$3$	$3$	$7.115$	3.3.837.1	$_{}$	None	None	✓	✓			891.2.a.m	$1$	$0$	$0$	$0$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots$
891.2.a.o	$891$	$2$	891.a	1.a	$1$	$4$	$4$	$7.115$	4.4.4752.1	$_{}$	None	None	✓	✓	✓		891.2.a.o	$1$	$1$	$-2$	$0$	$-8$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots$
891.2.a.p	$891$	$2$	891.a	1.a	$1$	$4$	$4$	$7.115$	4.4.22545.1	$_{}$	None	None	✓				99.2.e.e	$1$	$0$	$-1$	$0$	$-4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots$
891.2.a.q	$891$	$2$	891.a	1.a	$1$	$4$	$4$	$7.115$	4.4.22545.1	$_{}$	None	None	✓		✓		99.2.e.e	$1$	$0$	$1$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots$
891.2.a.r	$891$	$2$	891.a	1.a	$1$	$4$	$4$	$7.115$	4.4.4752.1	$_{}$	None	None	✓	✓			891.2.a.o	$1$	$0$	$2$	$0$	$8$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
891.2.d.a	$891$	$2$	891.d	33.d	$2$	$4$	$4$	$7.115$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None					99.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+4q^{16}+\cdots$
891.2.d.b	$891$	$2$	891.d	33.d	$2$	$16$	$16$	$7.115$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					99.2.g.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(2-\beta _{3})q^{4}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots$
891.2.d.c	$891$	$2$	891.d	33.d	$2$	$24$	$24$	$7.115$		$_{}$	None	None		✓	✓		891.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
891.2.e.a	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					297.2.a.a	$2$	$0$	$-2$	$0$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
891.2.e.b	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					11.2.a.a	$2$	$0$	$-2$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
891.2.e.c	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					99.2.a.a	$2$	$1$	$-1$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots$
891.2.e.d	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			891.2.a.b	$2$	$0$	$-1$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
891.2.e.e	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					33.2.a.a	$2$	$0$	$-1$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
891.2.e.f	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					297.2.a.b	$2$	$0$	$-1$	$0$	$2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
891.2.e.g	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					33.2.a.a	$2$	$0$	$1$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots$
891.2.e.h	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					297.2.a.b	$2$	$0$	$1$	$0$	$-2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots$
891.2.e.i	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			891.2.a.b	$2$	$0$	$1$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$
891.2.e.j	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					99.2.a.a	$2$	$0$	$1$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
891.2.e.k	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					11.2.a.a	$2$	$0$	$2$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
891.2.e.l	$891$	$2$	891.e	9.c	$3$	$2$	$1$	$7.115$	$\Q(\sqrt{-3}) $	$_{}$	None	None					297.2.a.a	$2$	$0$	$2$	$0$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
891.2.e.m	$891$	$2$	891.e	9.c	$3$	$4$	$2$	$7.115$	$\Q(\zeta_{12})$	$_{}$	None	None					297.2.a.e	$2$	$0$	$-2$	$0$	$-2$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{2}-\beta_1)q^{2}+(2\beta_{3}-2\beta_{2}+2\beta_1-2)q^{4}+\cdots$
891.2.e.n	$891$	$2$	891.e	9.c	$3$	$4$	$2$	$7.115$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			891.2.a.i	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
891.2.e.o	$891$	$2$	891.e	9.c	$3$	$4$	$2$	$7.115$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			891.2.a.i	$2$	$0$	$1$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
891.2.e.p	$891$	$2$	891.e	9.c	$3$	$4$	$2$	$7.115$	$\Q(\zeta_{12})$	$_{}$	None	None					297.2.a.e	$2$	$0$	$2$	$0$	$2$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_{2}+\beta_1)q^{2}+(2\beta_{3}-2\beta_{2}+2\beta_1-2)q^{4}+\cdots$
891.2.e.q	$891$	$2$	891.e	9.c	$3$	$6$	$3$	$7.115$	6.0.954288.1	$_{}$	None	None					297.2.a.g	$2$	$0$	$-1$	$0$	$2$	$-7$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$
891.2.e.r	$891$	$2$	891.e	9.c	$3$	$6$	$3$	$7.115$	6.0.2101707.2	$_{}$	None	None		✓			891.2.a.m	$2$	$0$	$0$	$0$	$-6$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots$
891.2.e.s	$891$	$2$	891.e	9.c	$3$	$6$	$3$	$7.115$	6.0.2101707.2	$_{}$	None	None		✓			891.2.a.m	$2$	$0$	$0$	$0$	$6$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots$
891.2.e.t	$891$	$2$	891.e	9.c	$3$	$6$	$3$	$7.115$	6.0.954288.1	$_{}$	None	None					297.2.a.g	$2$	$0$	$1$	$0$	$-2$	$-7$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
891.2.e.u	$891$	$2$	891.e	9.c	$3$	$8$	$4$	$7.115$	8.0.22581504.2	$_{}$	None	None		✓			891.2.a.o	$2$	$0$	$-2$	$0$	$-8$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
891.2.e.v	$891$	$2$	891.e	9.c	$3$	$8$	$4$	$7.115$	8.0.22581504.2	$_{}$	None	None		✓			891.2.a.o	$2$	$0$	$2$	$0$	$8$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots$
891.2.f.a	$891$	$2$	891.f	11.c	$5$	$4$	$1$	$7.115$	$\Q(\zeta_{10})$	$_{}$	None	None					99.2.m.a	$2$	$0$	$-4$	$0$	$6$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
891.2.f.b	$891$	$2$	891.f	11.c	$5$	$4$	$1$	$7.115$	$\Q(\zeta_{10})$	$_{}$	None	None					99.2.m.a	$2$	$0$	$4$	$0$	$-6$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(3+\cdots)q^{4}+\cdots$
891.2.f.c	$891$	$2$	891.f	11.c	$5$	$24$	$6$	$7.115$		$_{}$	None	None		✓			891.2.f.c	$2$	$0$	$-2$	$0$	$4$	$7$			$\mathrm{SU}(2)[C_{5}]$

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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.