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 239 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
100.1.j.a	$100$	$1$	100.j	100.j	$10$	$4$	$1$	$0.050$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	100.1.j.a	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
100.2.a.a	$100$	$2$	100.a	1.a	$1$	$1$	$1$	$0.799$	$\Q$	$_{}$	None	None	✓		✓	✓	20.2.a.a	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots$
100.2.c.a	$100$	$2$	100.c	5.b	$2$	$2$	$2$	$0.799$	$\Q(\sqrt{-1}) $	$_{}$	None	None			✓	✓	20.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{7}-q^{9}-\beta q^{13}-3\beta q^{17}+\cdots$
100.2.e.a	$100$	$2$	100.e	20.e	$4$	$2$	$1$	$0.799$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-5}) $	None		✓			100.2.e.a	$4$	$0$	$-2$	$-2$	$0$	$6$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i-1)q^{2}+(-i-1)q^{3}-2 i q^{4}+\cdots$
100.2.e.b	$100$	$2$	100.e	20.e	$4$	$2$	$1$	$0.799$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					20.2.e.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(2 i-2)q^{8}+\cdots$
100.2.e.c	$100$	$2$	100.e	20.e	$4$	$2$	$1$	$0.799$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-5}) $	None		✓			100.2.e.a	$4$	$0$	$2$	$2$	$0$	$-6$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i+1)q^{2}+(i+1)q^{3}-2 i q^{4}+\cdots$
100.2.e.d	$100$	$2$	100.e	20.e	$4$	$8$	$4$	$0.799$	8.0.3317760000.5	$_{}$	None	None		✓	✓		100.2.e.d	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots$
100.2.g.a	$100$	$2$	100.g	25.d	$5$	$12$	$3$	$0.799$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓	✓	100.2.g.a	$2$	$0$	$0$	$2$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{3}+(-1-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots$
100.2.i.a	$100$	$2$	100.i	25.e	$10$	$8$	$2$	$0.799$	8.0.58140625.2	$_{}$	None	None		✓	✓	✓	100.2.i.a	$2$	$0$	$0$	$0$	$5$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
100.2.l.a	$100$	$2$	100.l	100.l	$20$	$8$	$1$	$0.799$	$\Q(\zeta_{20})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			100.2.l.a	$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{20}]$	$q+(1-\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{2}+\cdots$
100.2.l.b	$100$	$2$	100.l	100.l	$20$	$96$	$12$	$0.799$		$_{}$	None	None		✓	✓		100.2.l.b	$4$	$0$	$-10$	$0$	$-20$	$0$			$\mathrm{SU}(2)[C_{20}]$
100.3.b.a	$100$	$3$	100.b	4.b	$2$	$1$	$1$	$2.725$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				20.3.d.c	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+24q^{13}+\cdots$
100.3.b.b	$100$	$3$	100.b	4.b	$2$	$1$	$1$	$2.725$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				20.3.d.c	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+8q^{8}+9q^{9}-24q^{13}+\cdots$
100.3.b.c	$100$	$3$	100.b	4.b	$2$	$2$	$2$	$2.725$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-5}) $	None					20.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+2\beta q^{3}-4 q^{4}-8 q^{6}+2\beta q^{7}+\cdots$
100.3.b.d	$100$	$3$	100.b	4.b	$2$	$4$	$4$	$2.725$	4.0.8405.1	$_{}$	None	None		✓			100.3.b.d	$2$	$0$	$-1$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
100.3.b.e	$100$	$3$	100.b	4.b	$2$	$4$	$4$	$2.725$	4.0.8405.1	$_{}$	None	None		✓			100.3.b.d	$2$	$0$	$1$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
100.3.b.f	$100$	$3$	100.b	4.b	$2$	$4$	$4$	$2.725$	$\Q(\zeta_{10})$	$_{}$	None	None					20.3.b.a	$2$	$0$	$2$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+\beta_{2} q^{3}+(\beta_{3}+\beta_{2}+\beta_1-1)q^{4}+\cdots$
100.3.d.a	$100$	$3$	100.d	20.d	$2$	$8$	$8$	$2.725$	8.0.$\cdots$.3	$_{}$	None	None		✓			100.3.b.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
100.3.d.b	$100$	$3$	100.d	20.d	$2$	$8$	$8$	$2.725$	$\Q(\zeta_{20})$	$_{}$	None	None					20.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+\beta_{6} q^{3}+(\beta_{4}+1)q^{4}+\cdots$
100.3.f.a	$100$	$3$	100.f	5.c	$4$	$2$	$1$	$2.725$	$\Q(\sqrt{-1}) $	$_{}$	None	None					20.3.f.a	$2$	$0$	$0$	$-2$	$0$	$14$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{3}+(7 i+7)q^{7}+7 i q^{9}+\cdots$
100.3.f.b	$100$	$3$	100.f	5.c	$4$	$4$	$2$	$2.725$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓	✓		100.3.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+3\beta _{1}q^{3}-4\beta _{3}q^{7}+18\beta _{2}q^{9}-15q^{11}+\cdots$
100.3.h.a	$100$	$3$	100.h	100.h	$10$	$8$	$2$	$2.725$	$\Q(\zeta_{20})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			100.3.h.a	$4$	$0$	$0$	$0$	$-6$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{10}]$	$q+\beta_1 q^{2}+4\beta_{2} q^{4}+(3\beta_{6}-3\beta_{4}+2\beta_{3}+\cdots-3)q^{5}+\cdots$
100.3.h.b	$100$	$3$	100.h	100.h	$10$	$104$	$26$	$2.725$		$_{}$	None	None		✓	✓		100.3.h.b	$4$	$0$	$-5$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
100.3.j.a	$100$	$3$	100.j	100.j	$10$	$112$	$28$	$2.725$		$_{}$	None	None		✓	✓	✓	100.3.j.a	$4$	$0$	$-3$	$0$	$-10$	$0$			$\mathrm{SU}(2)[C_{10}]$
100.3.k.a	$100$	$3$	100.k	25.f	$20$	$40$	$5$	$2.725$		$_{}$	None	None		✓	✓	✓	100.3.k.a	$2$	$0$	$0$	$-2$	$6$	$14$			$\mathrm{SU}(2)[C_{20}]$
100.4.a.a	$100$	$4$	100.a	1.a	$1$	$1$	$1$	$5.900$	$\Q$	$_{}$	None	None	✓				20.4.a.a	$1$	$1$	$0$	$-4$	$0$	$16$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}+2^{4}q^{7}-11q^{9}-60q^{11}+\cdots$
100.4.a.b	$100$	$4$	100.a	1.a	$1$	$1$	$1$	$5.900$	$\Q$	$_{}$	None	None	✓	✓			100.4.a.b	$1$	$1$	$0$	$-1$	$0$	$-26$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-26q^{7}-26q^{9}+45q^{11}-44q^{13}+\cdots$
100.4.a.c	$100$	$4$	100.a	1.a	$1$	$1$	$1$	$5.900$	$\Q$	$_{}$	None	None	✓	✓			100.4.a.b	$1$	$0$	$0$	$1$	$0$	$26$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+26q^{7}-26q^{9}+45q^{11}+44q^{13}+\cdots$
100.4.a.d	$100$	$4$	100.a	1.a	$1$	$2$	$2$	$5.900$	$\Q(\sqrt{19}) $	$_{}$	None	None	✓		✓		20.4.c.a	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{7}+7^{2}q^{9}+20q^{11}-6\beta q^{13}+\cdots$
100.4.c.a	$100$	$4$	100.c	5.b	$2$	$2$	$2$	$5.900$	$\Q(\sqrt{-1}) $	$_{}$	None	None					20.4.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{3}+8\beta q^{7}+11 q^{9}-60 q^{11}+\cdots$
100.4.c.b	$100$	$4$	100.c	5.b	$2$	$2$	$2$	$5.900$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			100.4.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-26 i q^{7}+26 q^{9}+45 q^{11}+\cdots$
100.4.e.a	$100$	$4$	100.e	20.e	$4$	$2$	$1$	$5.900$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					20.4.e.a	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2 i-2)q^{2}+8 i q^{4}+(-16 i+16)q^{8}+\cdots$
100.4.e.b	$100$	$4$	100.e	20.e	$4$	$2$	$1$	$5.900$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-5}) $	None		✓			100.4.e.b	$4$	$0$	$-4$	$14$	$0$	$-18$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(2 i-2)q^{2}+(7 i+7)q^{3}-8 i q^{4}+\cdots$
100.4.e.c	$100$	$4$	100.e	20.e	$4$	$2$	$1$	$5.900$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-5}) $	None		✓			100.4.e.b	$4$	$0$	$4$	$-14$	$0$	$18$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2 i+2)q^{2}+(-7 i-7)q^{3}+\cdots$
100.4.e.d	$100$	$4$	100.e	20.e	$4$	$8$	$4$	$5.900$	8.0.2342560000.1	$_{}$	None	None		✓			100.4.e.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{5}q^{2}+(-\beta _{3}-\beta _{6})q^{3}+(-\beta _{1}-3\beta _{4}+\cdots)q^{4}+\cdots$
100.4.e.e	$100$	$4$	100.e	20.e	$4$	$12$	$6$	$5.900$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					20.4.e.b	$4$	$0$	$6$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{3}+\beta _{5})q^{2}+\beta _{9}q^{3}+(-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
100.4.e.f	$100$	$4$	100.e	20.e	$4$	$24$	$12$	$5.900$		$_{}$	None	None		✓	✓		100.4.e.f	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
100.4.g.a	$100$	$4$	100.g	25.d	$5$	$28$	$7$	$5.900$		$_{}$	None	None		✓	✓	✓	100.4.g.a	$2$	$0$	$0$	$-4$	$-25$	$16$			$\mathrm{SU}(2)[C_{5}]$
100.4.i.a	$100$	$4$	100.i	25.e	$10$	$32$	$8$	$5.900$		$_{}$	None	None		✓	✓	✓	100.4.i.a	$2$	$0$	$0$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{10}]$
100.4.l.a	$100$	$4$	100.l	100.l	$20$	$8$	$1$	$5.900$	$\Q(\zeta_{20})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			100.4.l.a	$4$	$0$	$-4$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{20}]$	$q+(-2+2\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{2}+\cdots$
100.4.l.b	$100$	$4$	100.l	100.l	$20$	$336$	$42$	$5.900$		$_{}$	None	None		✓	✓		100.4.l.b	$4$	$0$	$-4$	$0$	$-20$	$0$			$\mathrm{SU}(2)[C_{20}]$
100.5.b.a	$100$	$5$	100.b	4.b	$2$	$1$	$1$	$10.337$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				4.5.b.a	$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}+2^{6}q^{8}+3^{4}q^{9}+238q^{13}+\cdots$
100.5.b.b	$100$	$5$	100.b	4.b	$2$	$2$	$2$	$10.337$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-5}) $	None					20.5.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta q^{2}+\beta q^{3}-16 q^{4}-8 q^{6}+\cdots$
100.5.b.c	$100$	$5$	100.b	4.b	$2$	$8$	$8$	$10.337$	8.0.$\cdots$.1	$_{}$	None	None					20.5.b.a	$2$	$0$	$-6$	$0$	$0$	$0$		$2^{15}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
100.5.b.d	$100$	$5$	100.b	4.b	$2$	$8$	$8$	$10.337$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			100.5.b.d	$2$	$0$	$-3$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots$
100.5.b.e	$100$	$5$	100.b	4.b	$2$	$8$	$8$	$10.337$	8.0.$\cdots$.1	$_{}$	None	None					20.5.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(6+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots$
100.5.b.f	$100$	$5$	100.b	4.b	$2$	$8$	$8$	$10.337$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			100.5.b.d	$2$	$0$	$3$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots$
100.5.d.a	$100$	$5$	100.d	20.d	$2$	$2$	$2$	$10.337$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					4.5.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta q^{2}-16 q^{4}-32\beta q^{8}-81 q^{9}+\cdots$
100.5.d.b	$100$	$5$	100.d	20.d	$2$	$16$	$16$	$10.337$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			100.5.b.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{24}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots$
100.5.d.c	$100$	$5$	100.d	20.d	$2$	$16$	$16$	$10.337$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					20.5.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{37}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{8}q^{3}+(2-\beta _{4})q^{4}+(6+\beta _{5}+\cdots)q^{6}+\cdots$

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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.