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 64 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
755.1.c.a	$755$	$1$	755.c	755.c	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-755}) $	None	✓	✓			755.1.c.a	$2$	$0$	$0$	$-1$	$1$	$2$		$1$		$q-q^{3}+q^{4}+q^{5}+2q^{7}-q^{11}-q^{12}+\cdots$
755.1.c.b	$755$	$1$	755.c	755.c	$2$	$1$	$1$	$0.377$	$\Q$	$D_{2}$	$\Q(\sqrt{-151}) $, $\Q(\sqrt{-755}) $	$\Q(\sqrt{5}) $	✓	✓			755.1.c.b	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+q^{4}-q^{5}-q^{9}+2q^{11}+q^{16}+2q^{19}+\cdots$
755.1.c.c	$755$	$1$	755.c	755.c	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-755}) $	None	✓	✓			755.1.c.a	$2$	$0$	$0$	$1$	$1$	$-2$		$1$		$q+q^{3}+q^{4}+q^{5}-2q^{7}-q^{11}+q^{12}+\cdots$
755.1.c.d	$755$	$1$	755.c	755.c	$2$	$2$	$2$	$0.377$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-755}) $	None	✓	✓			755.1.c.d	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{3}+q^{4}-q^{5}+2q^{9}-q^{11}-\beta q^{12}+\cdots$
755.1.c.e	$755$	$1$	755.c	755.c	$2$	$6$	$6$	$0.377$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-151}) $	None		✓	✓		755.1.c.e	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(-1-\zeta_{14}^{3}+\cdots)q^{4}+\cdots$
755.1.k.a	$755$	$1$	755.k	755.k	$6$	$2$	$1$	$0.377$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		✓	✓	✓	755.1.k.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}-q^{9}+\zeta_{6}q^{11}+\cdots$
755.1.o.a	$755$	$1$	755.o	755.o	$12$	$4$	$1$	$0.377$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	✓	✓	755.1.o.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{9}-\zeta_{12}^{2}q^{11}+\cdots$
755.2.a.a	$755$	$2$	755.a	1.a	$1$	$1$	$1$	$6.029$	$\Q$	$_{}$	None	None	✓	✓			755.2.a.a	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}+3q^{7}-3q^{9}+3q^{11}+\cdots$
755.2.a.b	$755$	$2$	755.a	1.a	$1$	$1$	$1$	$6.029$	$\Q$	$_{}$	None	None	✓	✓			755.2.a.b	$1$	$0$	$1$	$-2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}+2q^{7}+\cdots$
755.2.a.c	$755$	$2$	755.a	1.a	$1$	$1$	$1$	$6.029$	$\Q$	$_{}$	None	None	✓	✓			755.2.a.c	$1$	$1$	$1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots$
755.2.a.d	$755$	$2$	755.a	1.a	$1$	$1$	$1$	$6.029$	$\Q$	$_{}$	None	None	✓	✓			755.2.a.d	$1$	$0$	$2$	$-3$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+2q^{4}+q^{5}-6q^{6}+\cdots$
755.2.a.e	$755$	$2$	755.a	1.a	$1$	$1$	$1$	$6.029$	$\Q$	$_{}$	None	None	✓	✓			755.2.a.e	$1$	$0$	$2$	$1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+3q^{7}+\cdots$
755.2.a.f	$755$	$2$	755.a	1.a	$1$	$1$	$1$	$6.029$	$\Q$	$_{}$	None	None	✓	✓			755.2.a.f	$1$	$0$	$2$	$3$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots$
755.2.a.g	$755$	$2$	755.a	1.a	$1$	$2$	$2$	$6.029$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			755.2.a.g	$1$	$1$	$-2$	$-2$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}-q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots$
755.2.a.h	$755$	$2$	755.a	1.a	$1$	$5$	$5$	$6.029$	5.5.106069.1	$_{}$	None	None	✓	✓	✓		755.2.a.h	$1$	$1$	$-1$	$-2$	$5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(\beta _{1}-\beta _{4})q^{4}+q^{5}+\cdots$
755.2.a.i	$755$	$2$	755.a	1.a	$1$	$5$	$5$	$6.029$	5.5.220669.1	$_{}$	None	None	✓	✓	✓		755.2.a.i	$1$	$1$	$0$	$-3$	$-5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
755.2.a.j	$755$	$2$	755.a	1.a	$1$	$15$	$15$	$6.029$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓	✓		755.2.a.j	$1$	$0$	$-2$	$5$	$15$	$11$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
755.2.a.k	$755$	$2$	755.a	1.a	$1$	$18$	$18$	$6.029$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	✓	✓		755.2.a.k	$1$	$0$	$-2$	$2$	$-18$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{10}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots$
755.2.b.a	$755$	$2$	755.b	5.b	$2$	$4$	$4$	$6.029$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			755.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
755.2.b.b	$755$	$2$	755.b	5.b	$2$	$4$	$4$	$6.029$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			755.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots$
755.2.b.c	$755$	$2$	755.b	5.b	$2$	$22$	$22$	$6.029$		$_{}$	None	None		✓			755.2.b.c	$2$	$0$	$0$	$0$	$-1$	$0$			$\mathrm{SU}(2)[C_{2}]$
755.2.b.d	$755$	$2$	755.b	5.b	$2$	$44$	$44$	$6.029$		$_{}$	None	None		✓	✓		755.2.b.d	$2$	$0$	$0$	$0$	$-1$	$0$			$\mathrm{SU}(2)[C_{2}]$
755.2.e.a	$755$	$2$	755.e	151.c	$3$	$2$	$1$	$6.029$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			755.2.e.a	$2$	$0$	$1$	$-4$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-2q^{3}+\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots$
755.2.e.b	$755$	$2$	755.e	151.c	$3$	$4$	$2$	$6.029$	$\Q(\sqrt{-3}, \sqrt{37})$	$_{}$	None	None		✓			755.2.e.b	$2$	$0$	$-2$	$4$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots$
755.2.e.c	$755$	$2$	755.e	151.c	$3$	$4$	$2$	$6.029$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			755.2.e.c	$2$	$0$	$0$	$0$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\beta _{1}+\beta _{3})q^{2}+(1+2\beta _{2})q^{3}+\cdots$
755.2.e.d	$755$	$2$	755.e	151.c	$3$	$8$	$4$	$6.029$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			755.2.e.d	$2$	$0$	$4$	$-4$	$-4$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+\beta _{3}q^{3}+(1-\beta _{4})q^{4}-\beta _{4}q^{5}+\cdots$
755.2.e.e	$755$	$2$	755.e	151.c	$3$	$40$	$20$	$6.029$		$_{}$	None	None		✓			755.2.e.e	$2$	$0$	$-3$	$12$	$-20$	$-6$			$\mathrm{SU}(2)[C_{3}]$
755.2.e.f	$755$	$2$	755.e	151.c	$3$	$42$	$21$	$6.029$		$_{}$	None	None		✓	✓		755.2.e.f	$2$	$0$	$2$	$-4$	$21$	$7$			$\mathrm{SU}(2)[C_{3}]$
755.2.f.a	$755$	$2$	755.f	755.f	$4$	$4$	$2$	$6.029$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			755.2.f.a	$4$	$0$	$-4$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+\cdots$
755.2.f.b	$755$	$2$	755.f	755.f	$4$	$4$	$2$	$6.029$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			755.2.f.b	$4$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}-2\beta _{2}q^{4}+(-2-\beta _{2})q^{5}+\cdots$
755.2.f.c	$755$	$2$	755.f	755.f	$4$	$4$	$2$	$6.029$	$\Q(i, \sqrt{14})$	$_{}$	None	None		✓			755.2.f.c	$4$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}-2\beta _{2}q^{4}+(2-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$
755.2.f.d	$755$	$2$	755.f	755.f	$4$	$28$	$14$	$6.029$		$_{}$	$\Q(\sqrt{-151}) $	None		✓			755.2.f.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{4}]$
755.2.f.e	$755$	$2$	755.f	755.f	$4$	$108$	$54$	$6.029$		$_{}$	None	None		✓	✓		755.2.f.e	$4$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{4}]$
755.2.h.a	$755$	$2$	755.h	151.d	$5$	$4$	$1$	$6.029$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			755.2.h.a	$2$	$1$	$-6$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}+\cdots)q^{3}+\cdots$
755.2.h.b	$755$	$2$	755.h	151.d	$5$	$4$	$1$	$6.029$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			755.2.h.b	$2$	$0$	$-2$	$-6$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+2\zeta_{10}^{3})q^{3}+\cdots$
755.2.h.c	$755$	$2$	755.h	151.d	$5$	$4$	$1$	$6.029$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			755.2.h.c	$2$	$0$	$-2$	$-2$	$-1$	$-9$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+2\zeta_{10}+\cdots)q^{3}+\cdots$
755.2.h.d	$755$	$2$	755.h	151.d	$5$	$16$	$4$	$6.029$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			755.2.h.d	$2$	$0$	$-4$	$-4$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{7}-\beta _{13})q^{2}+(-\beta _{7}+\beta _{14})q^{3}+\cdots$
755.2.h.e	$755$	$2$	755.h	151.d	$5$	$80$	$20$	$6.029$		$_{}$	None	None		✓			755.2.h.e	$2$	$0$	$12$	$13$	$20$	$4$			$\mathrm{SU}(2)[C_{5}]$
755.2.h.f	$755$	$2$	755.h	151.d	$5$	$100$	$25$	$6.029$		$_{}$	None	None		✓	✓		755.2.h.f	$2$	$0$	$-2$	$-4$	$-25$	$-5$			$\mathrm{SU}(2)[C_{5}]$
755.2.j.a	$755$	$2$	755.j	755.j	$6$	$148$	$74$	$6.029$		$_{}$	None	None		✓	✓	✓	755.2.j.a	$4$	$0$	$0$	$0$	$-1$	$0$			$\mathrm{SU}(2)[C_{6}]$
755.2.m.a	$755$	$2$	755.m	755.m	$10$	$296$	$74$	$6.029$		$_{}$	None	None		✓	✓	✓	755.2.m.a	$4$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{10}]$
755.2.p.a	$755$	$2$	755.p	755.p	$12$	$296$	$74$	$6.029$		$_{}$	None	None		✓	✓	✓	755.2.p.a	$4$	$0$	$-2$	$0$	$-2$	$-18$			$\mathrm{SU}(2)[C_{12}]$
755.2.q.a	$755$	$2$	755.q	151.g	$15$	$200$	$25$	$6.029$		$_{}$	None	None		✓			755.2.q.a	$2$	$0$	$-2$	$-4$	$25$	$3$			$\mathrm{SU}(2)[C_{15}]$
755.2.q.b	$755$	$2$	755.q	151.g	$15$	$200$	$25$	$6.029$		$_{}$	None	None		✓			755.2.q.b	$2$	$0$	$0$	$0$	$-25$	$-3$			$\mathrm{SU}(2)[C_{15}]$
755.2.s.a	$755$	$2$	755.s	755.s	$20$	$592$	$74$	$6.029$		$_{}$	None	None		✓	✓	✓	755.2.s.a	$4$	$0$	$-16$	$-10$	$-6$	$-10$			$\mathrm{SU}(2)[C_{20}]$
755.2.t.a	$755$	$2$	755.t	151.h	$25$	$520$	$26$	$6.029$		$_{}$	None	None		✓			755.2.t.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{25}]$
755.2.t.b	$755$	$2$	755.t	151.h	$25$	$520$	$26$	$6.029$		$_{}$	None	None		✓			755.2.t.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{25}]$
755.2.w.a	$755$	$2$	755.w	755.w	$30$	$592$	$74$	$6.029$		$_{}$	None	None		✓	✓	✓	755.2.w.a	$4$	$0$	$0$	$0$	$-9$	$0$			$\mathrm{SU}(2)[C_{30}]$
755.2.z.a	$755$	$2$	755.z	755.z	$50$	$1480$	$74$	$6.029$		$_{}$	None	None		✓	✓	✓	755.2.z.a	$4$	$0$	$0$	$0$	$-20$	$0$			$\mathrm{SU}(2)[C_{50}]$
755.2.ba.a	$755$	$2$	755.ba	755.aa	$60$	$1184$	$74$	$6.029$		$_{}$	None	None		✓	✓	✓	755.2.ba.a	$4$	$0$	$-8$	$-20$	$-18$	$-2$			$\mathrm{SU}(2)[C_{60}]$

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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.