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 215 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
990.2.a.a	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓	✓	✓	✓	990.2.a.a	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-q^{11}+\cdots$
990.2.a.b	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓				330.2.a.d	$1$	$0$	$-1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-q^{11}+\cdots$
990.2.a.c	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓		✓	✓	330.2.a.e	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots$
990.2.a.d	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓				110.2.a.b	$1$	$0$	$-1$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots$
990.2.a.e	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓	✓	✓	✓	990.2.a.e	$1$	$0$	$-1$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
990.2.a.f	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓				110.2.a.c	$1$	$0$	$-1$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
990.2.a.g	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓				330.2.a.c	$1$	$0$	$-1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
990.2.a.h	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓		✓	✓	330.2.a.b	$1$	$1$	$1$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
990.2.a.i	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓	✓	✓	✓	990.2.a.e	$1$	$1$	$1$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
990.2.a.j	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓				330.2.a.a	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
990.2.a.k	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓	✓	✓	✓	990.2.a.a	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
990.2.a.l	$990$	$2$	990.a	1.a	$1$	$1$	$1$	$7.905$	$\Q$	None	✓				110.2.a.a	$1$	$0$	$1$	$0$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+5q^{7}+q^{8}+q^{10}+\cdots$
990.2.a.m	$990$	$2$	990.a	1.a	$1$	$2$	$2$	$7.905$	$\Q(\sqrt{33}) $	None	✓		✓	✓	110.2.a.d	$1$	$0$	$2$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots$
990.2.c.a	$990$	$2$	990.c	5.b	$2$	$2$	$2$	$7.905$	$\Q(\sqrt{-1}) $	None		✓			990.2.c.a	$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(-i-2)q^{5}+4 i q^{7}+\cdots$
990.2.c.b	$990$	$2$	990.c	5.b	$2$	$2$	$2$	$7.905$	$\Q(\sqrt{-1}) $	None					110.2.b.c	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(-i-2)q^{5}+i q^{7}+\cdots$
990.2.c.c	$990$	$2$	990.c	5.b	$2$	$2$	$2$	$7.905$	$\Q(\sqrt{-1}) $	None					110.2.b.b	$2$	$1$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(2 i-1)q^{5}+i q^{8}+\cdots$
990.2.c.d	$990$	$2$	990.c	5.b	$2$	$2$	$2$	$7.905$	$\Q(\sqrt{-1}) $	None					110.2.b.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(-i+2)q^{5}+3 i q^{7}+\cdots$
990.2.c.e	$990$	$2$	990.c	5.b	$2$	$2$	$2$	$7.905$	$\Q(\sqrt{-1}) $	None		✓			990.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(i+2)q^{5}+4 i q^{7}+\cdots$
990.2.c.f	$990$	$2$	990.c	5.b	$2$	$4$	$4$	$7.905$	$\Q(i, \sqrt{6})$	None		✓			990.2.c.f	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$
990.2.c.g	$990$	$2$	990.c	5.b	$2$	$4$	$4$	$7.905$	$\Q(i, \sqrt{10})$	None					330.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{4}+\beta _{3}q^{5}+(-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$
990.2.c.h	$990$	$2$	990.c	5.b	$2$	$4$	$4$	$7.905$	$\Q(\zeta_{8})$	None					330.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
990.2.c.i	$990$	$2$	990.c	5.b	$2$	$4$	$4$	$7.905$	$\Q(i, \sqrt{6})$	None		✓			990.2.c.f	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
990.2.d.a	$990$	$2$	990.d	33.d	$2$	$8$	$8$	$7.905$	8.0.4328587264.1	None		✓			990.2.d.a	$2$	$0$	$-8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+(-\beta _{5}-\beta _{7})q^{7}+\cdots$
990.2.d.b	$990$	$2$	990.d	33.d	$2$	$8$	$8$	$7.905$	8.0.4328587264.1	None		✓			990.2.d.a	$2$	$0$	$8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(-\beta _{5}-\beta _{7})q^{7}+\cdots$
990.2.f.a	$990$	$2$	990.f	165.d	$2$	$4$	$4$	$7.905$	$\Q(\zeta_{8})$	None		✓			990.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}-q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
990.2.f.b	$990$	$2$	990.f	165.d	$2$	$4$	$4$	$7.905$	$\Q(\zeta_{8})$	None		✓			990.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+(3\zeta_{8}+\cdots)q^{7}+\cdots$
990.2.f.c	$990$	$2$	990.f	165.d	$2$	$16$	$16$	$7.905$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		990.2.f.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-q^{4}+\beta _{10}q^{5}-\beta _{4}q^{7}-\beta _{8}q^{8}+\cdots$
990.2.i.a	$990$	$2$	990.i	9.c	$3$	$2$	$1$	$7.905$	$\Q(\sqrt{-3}) $	None		✓			990.2.i.a	$2$	$0$	$-1$	$3$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
990.2.i.b	$990$	$2$	990.i	9.c	$3$	$2$	$1$	$7.905$	$\Q(\sqrt{-3}) $	None		✓			990.2.i.b	$2$	$0$	$1$	$-3$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
990.2.i.c	$990$	$2$	990.i	9.c	$3$	$6$	$3$	$7.905$	6.0.309123.1	None		✓			990.2.i.c	$2$	$0$	$-3$	$-4$	$-3$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}+(-1+\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots$
990.2.i.d	$990$	$2$	990.i	9.c	$3$	$6$	$3$	$7.905$	$\Q(\zeta_{18})$	None		✓			990.2.i.d	$2$	$0$	$-3$	$0$	$3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_1 q^{2}+(\beta_{4}+\beta_{3}-\beta_{2})q^{3}+(\beta_1-1)q^{4}+\cdots$
990.2.i.e	$990$	$2$	990.i	9.c	$3$	$6$	$3$	$7.905$	6.0.309123.1	None		✓			990.2.i.e	$2$	$0$	$3$	$-2$	$3$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots$
990.2.i.f	$990$	$2$	990.i	9.c	$3$	$6$	$3$	$7.905$	$\Q(\zeta_{18})$	None		✓			990.2.i.f	$2$	$0$	$3$	$0$	$3$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{2}+(\beta_{5}-\beta_{3})q^{3}+(\beta_1-1)q^{4}+\cdots$
990.2.i.g	$990$	$2$	990.i	9.c	$3$	$6$	$3$	$7.905$	6.0.309123.1	None		✓			990.2.i.g	$2$	$0$	$3$	$2$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
990.2.i.h	$990$	$2$	990.i	9.c	$3$	$6$	$3$	$7.905$	6.0.309123.1	None		✓			990.2.i.h	$2$	$0$	$3$	$4$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}+(1-\beta _{5})q^{3}+\beta _{4}q^{4}+\cdots$
990.2.i.i	$990$	$2$	990.i	9.c	$3$	$12$	$6$	$7.905$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			990.2.i.i	$2$	$0$	$-6$	$0$	$6$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{2}+\beta _{10}q^{3}+(-1+\beta _{6})q^{4}+\cdots$
990.2.i.j	$990$	$2$	990.i	9.c	$3$	$14$	$7$	$7.905$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			990.2.i.j	$2$	$0$	$-7$	$-1$	$-7$	$-5$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{6})q^{2}+\beta _{2}q^{3}-\beta _{6}q^{4}-\beta _{6}q^{5}+\cdots$
990.2.i.k	$990$	$2$	990.i	9.c	$3$	$14$	$7$	$7.905$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			990.2.i.k	$2$	$0$	$7$	$1$	$-7$	$-5$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{3})q^{2}+\beta _{7}q^{3}-\beta _{3}q^{4}-\beta _{3}q^{5}+\cdots$
990.2.k.a	$990$	$2$	990.k	15.e	$4$	$8$	$4$	$7.905$	$\Q(\zeta_{16})$	None		✓			990.2.k.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(-\zeta_{16}-2\zeta_{16}^{5}+\cdots)q^{5}+\cdots$
990.2.k.b	$990$	$2$	990.k	15.e	$4$	$8$	$4$	$7.905$	$\Q(\zeta_{16})$	None		✓			990.2.k.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(\zeta_{16}+2\zeta_{16}^{5}+\cdots)q^{5}+\cdots$
990.2.k.c	$990$	$2$	990.k	15.e	$4$	$12$	$6$	$7.905$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			990.2.k.c	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}-\beta _{2}q^{4}+\beta _{11}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
990.2.k.d	$990$	$2$	990.k	15.e	$4$	$12$	$6$	$7.905$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			990.2.k.c	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{2}-\beta _{2}q^{4}-\beta _{11}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
990.2.m.a	$990$	$2$	990.m	55.e	$4$	$4$	$2$	$7.905$	$\Q(\zeta_{8})$	None					110.2.f.a	$4$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2+\zeta_{8}^{2})q^{5}+\cdots$
990.2.m.b	$990$	$2$	990.m	55.e	$4$	$4$	$2$	$7.905$	$\Q(\zeta_{8})$	None					330.2.l.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
990.2.m.c	$990$	$2$	990.m	55.e	$4$	$4$	$2$	$7.905$	$\Q(\zeta_{8})$	None					110.2.f.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
990.2.m.d	$990$	$2$	990.m	55.e	$4$	$4$	$2$	$7.905$	$\Q(\zeta_{8})$	None					110.2.f.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
990.2.m.e	$990$	$2$	990.m	55.e	$4$	$4$	$2$	$7.905$	$\Q(\zeta_{8})$	None					330.2.l.a	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
990.2.m.f	$990$	$2$	990.m	55.e	$4$	$8$	$4$	$7.905$	8.0.822083584.4	None					330.2.l.c	$2$	$0$	$0$	$0$	$8$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}+\beta _{4}q^{4}+(1-\beta _{6}-\beta _{7})q^{5}+\cdots$
990.2.m.g	$990$	$2$	990.m	55.e	$4$	$8$	$4$	$7.905$	8.0.822083584.4	None					330.2.l.c	$2$	$0$	$0$	$0$	$8$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}-\beta _{4}q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
990.2.m.h	$990$	$2$	990.m	55.e	$4$	$24$	$12$	$7.905$		None		✓	✓		990.2.m.h	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.