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 (47 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
1127.1.d.a	$1127$	$1$	1127.d	23.b	$2$	$1$	$1$	$0.562$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-23}) $	$\Q(\sqrt{161}) $	✓	✓			1127.1.d.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-2q^{2}+3q^{4}-4q^{8}-q^{9}+5q^{16}+\cdots$
1127.1.d.b	$1127$	$1$	1127.d	23.b	$2$	$1$	$1$	$0.562$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓				23.1.b.a	$2$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}-q^{6}+q^{8}+q^{13}-q^{16}+\cdots$
1127.1.d.c	$1127$	$1$	1127.d	23.b	$2$	$2$	$2$	$0.562$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None	✓	✓			1127.1.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}-q^{4}+q^{9}+\beta q^{12}-\beta q^{13}+\cdots$
1127.1.d.d	$1127$	$1$	1127.d	23.b	$2$	$2$	$2$	$0.562$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None	✓	✓			1127.1.d.d	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}-\beta q^{3}-\beta q^{6}-q^{8}+2q^{9}+\beta q^{13}+\cdots$
1127.1.d.e	$1127$	$1$	1127.d	23.b	$2$	$4$	$4$	$0.562$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-23}) $	None	✓	✓	✓		1127.1.d.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}+2q^{4}+(2\beta _{1}+\beta _{3})q^{6}+\cdots$
1127.1.f.a	$1127$	$1$	1127.f	161.f	$6$	$2$	$1$	$0.562$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-23}) $	None					23.1.b.a	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}-q^{6}+q^{8}+q^{13}+\cdots$
1127.1.f.b	$1127$	$1$	1127.f	161.f	$6$	$2$	$1$	$0.562$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-23}) $	None					23.1.b.a	$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+q^{6}+q^{8}-q^{13}+\cdots$
1127.1.f.c	$1127$	$1$	1127.f	161.f	$6$	$2$	$1$	$0.562$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-23}) $	$\Q(\sqrt{161}) $		✓			1127.1.d.a	$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{2}+3\zeta_{6}^{2}q^{4}+2q^{8}+\zeta_{6}q^{9}+\cdots$
1127.1.f.d	$1127$	$1$	1127.f	161.f	$6$	$4$	$2$	$0.562$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-23}) $	None		✓			1127.1.d.d	$8$	$0$	$-2$	$0$	$0$	$0$		$3$		$q+\zeta_{12}^{4}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\cdots)q^{6}+\cdots$
1127.1.f.e	$1127$	$1$	1127.f	161.f	$6$	$4$	$2$	$0.562$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-23}) $	None		✓			1127.1.d.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{9}+(-\beta _{1}+\cdots)q^{12}+\cdots$
1127.1.f.f	$1127$	$1$	1127.f	161.f	$6$	$8$	$4$	$0.562$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		✓	✓		1127.1.d.e	$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$		$q+(\zeta_{24}^{6}+\zeta_{24}^{10})q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11}+\cdots)q^{3}+\cdots$
1127.1.o.a	$1127$	$1$	1127.o	23.d	$22$	$10$	$1$	$0.562$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	1127.1.o.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(-\zeta_{22}^{6}+\zeta_{22}^{9})q^{2}+(-\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
1127.1.v.a	$1127$	$1$	1127.v	161.n	$66$	$20$	$1$	$0.562$	$\Q(\zeta_{33})$	$D_{11}$	$\Q(\sqrt{-7}) $	None			✓	✓	161.1.l.a	$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(-\zeta_{66}^{23}-\zeta_{66}^{29})q^{2}+(-\zeta_{66}^{13}+\cdots)q^{4}+\cdots$
1127.1.x.a	$1127$	$1$	1127.x	161.p	$66$	$20$	$1$	$0.562$	$\Q(\zeta_{33})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	1127.1.o.a	$8$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+(\zeta_{66}^{5}+\zeta_{66}^{29})q^{2}+(-\zeta_{66}+\zeta_{66}^{10}+\cdots)q^{4}+\cdots$
1127.2.a.a	$1127$	$2$	1127.a	1.a	$1$	$1$	$1$	$8.999$	$\Q$	$_{}$	None	None	✓				161.2.a.a	$1$	$0$	$-1$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+3q^{8}-3q^{9}+2q^{10}+\cdots$
1127.2.a.b	$1127$	$2$	1127.a	1.a	$1$	$2$	$2$	$8.999$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1127.2.a.b	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}-q^{4}-\beta q^{5}+\beta q^{6}+3q^{8}+\cdots$
1127.2.a.c	$1127$	$2$	1127.a	1.a	$1$	$2$	$2$	$8.999$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				23.2.a.a	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
1127.2.a.d	$1127$	$2$	1127.a	1.a	$1$	$2$	$2$	$8.999$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				161.2.a.b	$1$	$0$	$-1$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots$
1127.2.a.e	$1127$	$2$	1127.a	1.a	$1$	$2$	$2$	$8.999$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1127.2.a.e	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}-q^{4}+\beta q^{5}+\beta q^{6}-3q^{8}+\cdots$
1127.2.a.f	$1127$	$2$	1127.a	1.a	$1$	$3$	$3$	$8.999$	3.3.148.1	$_{}$	None	None	✓				161.2.a.c	$1$	$1$	$-1$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots$
1127.2.a.g	$1127$	$2$	1127.a	1.a	$1$	$4$	$4$	$8.999$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	✓			1127.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots$
1127.2.a.h	$1127$	$2$	1127.a	1.a	$1$	$5$	$5$	$8.999$	5.5.2147108.1	$_{}$	None	None	✓				161.2.a.d	$1$	$0$	$2$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots$
1127.2.a.i	$1127$	$2$	1127.a	1.a	$1$	$6$	$6$	$8.999$	6.6.2803712.1	$_{}$	None	None	✓	✓			1127.2.a.i	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots$
1127.2.a.j	$1127$	$2$	1127.a	1.a	$1$	$6$	$6$	$8.999$	6.6.89672832.1	$_{}$	None	None	✓	✓			1127.2.a.j	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{4}q^{3}+(2+\beta _{5})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
1127.2.a.k	$1127$	$2$	1127.a	1.a	$1$	$7$	$7$	$8.999$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓		✓		161.2.e.a	$1$	$1$	$0$	$-5$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1127.2.a.l	$1127$	$2$	1127.a	1.a	$1$	$7$	$7$	$8.999$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓		✓		161.2.e.b	$1$	$1$	$0$	$-3$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
1127.2.a.m	$1127$	$2$	1127.a	1.a	$1$	$7$	$7$	$8.999$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓		✓		161.2.e.b	$1$	$0$	$0$	$3$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
1127.2.a.n	$1127$	$2$	1127.a	1.a	$1$	$7$	$7$	$8.999$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				161.2.e.a	$1$	$0$	$0$	$5$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1127.2.a.o	$1127$	$2$	1127.a	1.a	$1$	$14$	$14$	$8.999$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	✓	✓		1127.2.a.o	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{9}q^{2}+\beta _{1}q^{3}+(2+\beta _{7})q^{4}+\beta _{5}q^{5}+\cdots$
1127.2.c.a	$1127$	$2$	1127.c	161.c	$2$	$24$	$24$	$8.999$		$_{}$	None	None		✓			1127.2.c.a	$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1127.2.c.b	$1127$	$2$	1127.c	161.c	$2$	$24$	$24$	$8.999$		$_{}$	$\Q(\sqrt{-23}) $	None		✓			1127.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{2}]$
1127.2.c.c	$1127$	$2$	1127.c	161.c	$2$	$28$	$28$	$8.999$		$_{}$	None	None			✓		161.2.g.a	$4$	$0$	$8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1127.4.a.a	$1127$	$4$	1127.a	1.a	$1$	$1$	$1$	$66.495$	$\Q$	$_{}$	None	None	✓				23.4.a.a	$1$	$0$	$-2$	$5$	$6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+5q^{3}-4q^{4}+6q^{5}-10q^{6}+\cdots$
1127.4.a.b	$1127$	$4$	1127.a	1.a	$1$	$2$	$2$	$66.495$	$\Q(\sqrt{23}) $	$_{}$	None	None	✓	✓			1127.4.a.b	$2$	$1$	$4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta q^{3}-4q^{4}+4\beta q^{5}+2\beta q^{6}+\cdots$
1127.4.a.c	$1127$	$4$	1127.a	1.a	$1$	$4$	$4$	$66.495$	4.4.334189.1	$_{}$	None	None	✓				23.4.a.b	$1$	$1$	$2$	$-7$	$-14$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots$
1127.4.a.d	$1127$	$4$	1127.a	1.a	$1$	$5$	$5$	$66.495$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓				161.4.a.a	$1$	$1$	$-4$	$11$	$4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
1127.4.a.e	$1127$	$4$	1127.a	1.a	$1$	$8$	$8$	$66.495$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				161.4.a.b	$1$	$0$	$0$	$3$	$24$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(3+\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
1127.4.a.f	$1127$	$4$	1127.a	1.a	$1$	$9$	$9$	$66.495$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓				161.4.a.c	$1$	$1$	$0$	$-9$	$4$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(5+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1127.4.a.g	$1127$	$4$	1127.a	1.a	$1$	$12$	$12$	$66.495$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓			1127.4.a.g	$2$	$1$	$-4$	$0$	$0$	$0$	$-$	$2^{12}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{9}q^{3}+(4-\beta _{2}-\beta _{4})q^{4}+\cdots$
1127.4.a.h	$1127$	$4$	1127.a	1.a	$1$	$12$	$12$	$66.495$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓				161.4.a.d	$1$	$0$	$4$	$-1$	$-16$	$0$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(6+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1127.4.a.i	$1127$	$4$	1127.a	1.a	$1$	$20$	$20$	$66.495$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	✓			1127.4.a.i	$2$	$0$	$8$	$0$	$0$	$0$	$+$	$2^{20}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(4-\beta _{3}-\beta _{4})q^{4}+\cdots$
1127.4.a.j	$1127$	$4$	1127.a	1.a	$1$	$22$	$22$	$66.495$		$_{}$	None	None	✓				161.4.e.b	$1$	$1$	$0$	$-18$	$-20$	$0$	$-$		$\mathrm{SU}(2)$
1127.4.a.k	$1127$	$4$	1127.a	1.a	$1$	$22$	$22$	$66.495$		$_{}$	None	None	✓		✓		161.4.e.a	$1$	$1$	$0$	$-6$	$-20$	$0$	$-$		$\mathrm{SU}(2)$
1127.4.a.l	$1127$	$4$	1127.a	1.a	$1$	$22$	$22$	$66.495$		$_{}$	None	None	✓				161.4.e.a	$1$	$0$	$0$	$6$	$20$	$0$	$+$		$\mathrm{SU}(2)$
1127.4.a.m	$1127$	$4$	1127.a	1.a	$1$	$22$	$22$	$66.495$		$_{}$	None	None	✓		✓		161.4.e.b	$1$	$0$	$0$	$18$	$20$	$0$	$+$		$\mathrm{SU}(2)$
1127.4.a.n	$1127$	$4$	1127.a	1.a	$1$	$26$	$26$	$66.495$		$_{}$	None	None	✓	✓	✓		1127.4.a.n	$2$	$1$	$-12$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$
1127.4.a.o	$1127$	$4$	1127.a	1.a	$1$	$38$	$38$	$66.495$		$_{}$	None	None	✓	✓	✓		1127.4.a.o	$2$	$0$	$4$	$0$	$0$	$0$	$+$		$\mathrm{SU}(2)$

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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.