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 153 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
370.2.a.a	$370$	$2$	370.a	1.a	$1$	$1$	$1$	$2.954$	$\Q$	None	✓	✓	✓	✓	370.2.a.a	$1$	$0$	$-1$	$-2$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-q^{7}+\cdots$
370.2.a.b	$370$	$2$	370.a	1.a	$1$	$1$	$1$	$2.954$	$\Q$	None	✓	✓	✓	✓	370.2.a.b	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots$
370.2.a.c	$370$	$2$	370.a	1.a	$1$	$1$	$1$	$2.954$	$\Q$	None	✓	✓	✓	✓	370.2.a.c	$1$	$0$	$-1$	$2$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
370.2.a.d	$370$	$2$	370.a	1.a	$1$	$1$	$1$	$2.954$	$\Q$	None	✓	✓			370.2.a.d	$1$	$0$	$1$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots$
370.2.a.e	$370$	$2$	370.a	1.a	$1$	$2$	$2$	$2.954$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	370.2.a.e	$1$	$1$	$-2$	$-2$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots$
370.2.a.f	$370$	$2$	370.a	1.a	$1$	$2$	$2$	$2.954$	$\Q(\sqrt{33}) $	None	✓	✓	✓		370.2.a.f	$1$	$0$	$2$	$4$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+(-1+\cdots)q^{7}+\cdots$
370.2.a.g	$370$	$2$	370.a	1.a	$1$	$3$	$3$	$2.954$	3.3.892.1	None	✓	✓	✓	✓	370.2.a.g	$1$	$0$	$3$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}-q^{5}-\beta _{2}q^{6}+\cdots$
370.2.b.a	$370$	$2$	370.b	5.b	$2$	$2$	$2$	$2.954$	$\Q(\sqrt{-1}) $	None		✓			370.2.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(-i-2)q^{5}-2 i q^{7}+\cdots$
370.2.b.b	$370$	$2$	370.b	5.b	$2$	$2$	$2$	$2.954$	$\Q(\sqrt{-1}) $	None		✓			370.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(2 i+1)q^{5}+i q^{7}+\cdots$
370.2.b.c	$370$	$2$	370.b	5.b	$2$	$4$	$4$	$2.954$	$\Q(i, \sqrt{6})$	None		✓			370.2.b.c	$2$	$0$	$0$	$0$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
370.2.b.d	$370$	$2$	370.b	5.b	$2$	$10$	$10$	$2.954$	10.0.$\cdots$.1	None		✓	✓		370.2.b.d	$2$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{4}-\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
370.2.c.a	$370$	$2$	370.c	185.d	$2$	$10$	$10$	$2.954$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓			370.2.c.a	$2$	$0$	$-10$	$0$	$-3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
370.2.c.b	$370$	$2$	370.c	185.d	$2$	$10$	$10$	$2.954$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓			370.2.c.a	$2$	$0$	$10$	$0$	$3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$
370.2.d.a	$370$	$2$	370.d	37.b	$2$	$2$	$2$	$2.954$	$\Q(\sqrt{-1}) $	None		✓			370.2.d.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+i q^{5}-2 q^{7}-i q^{8}+\cdots$
370.2.d.b	$370$	$2$	370.d	37.b	$2$	$2$	$2$	$2.954$	$\Q(\sqrt{-1}) $	None		✓			370.2.d.b	$2$	$0$	$0$	$0$	$0$	$10$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+i q^{5}+5 q^{7}-i q^{8}+\cdots$
370.2.d.c	$370$	$2$	370.d	37.b	$2$	$6$	$6$	$2.954$	6.0.399424.1	None		✓	✓		370.2.d.c	$2$	$0$	$0$	$-4$	$0$	$10$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}-q^{4}+\cdots$
370.2.e.a	$370$	$2$	370.e	37.c	$3$	$2$	$1$	$2.954$	$\Q(\sqrt{-3}) $	None		✓			370.2.e.a	$2$	$0$	$1$	$-2$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
370.2.e.b	$370$	$2$	370.e	37.c	$3$	$2$	$1$	$2.954$	$\Q(\sqrt{-3}) $	None		✓			370.2.e.b	$2$	$0$	$1$	$-1$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
370.2.e.c	$370$	$2$	370.e	37.c	$3$	$2$	$1$	$2.954$	$\Q(\sqrt{-3}) $	None		✓			370.2.e.c	$2$	$0$	$1$	$3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+3\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
370.2.e.d	$370$	$2$	370.e	37.c	$3$	$4$	$2$	$2.954$	$\Q(\zeta_{12})$	None		✓			370.2.e.d	$2$	$0$	$-2$	$2$	$-2$	$0$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_1-1)q^{2}+\beta_1 q^{3}-\beta_1 q^{4}+\cdots$
370.2.e.e	$370$	$2$	370.e	37.c	$3$	$4$	$2$	$2.954$	$\Q(\sqrt{-3}, \sqrt{10})$	None		✓			370.2.e.e	$2$	$0$	$2$	$2$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots$
370.2.e.f	$370$	$2$	370.e	37.c	$3$	$6$	$3$	$2.954$	6.0.2696112.1	None		✓	✓		370.2.e.f	$2$	$0$	$-3$	$0$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots$
370.2.g.a	$370$	$2$	370.g	185.f	$4$	$2$	$1$	$2.954$	$\Q(\sqrt{-1}) $	None		✓			370.2.g.a	$2$	$0$	$0$	$-2$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{2}+(-i-1)q^{3}-q^{4}+(i+2)q^{5}+\cdots$
370.2.g.b	$370$	$2$	370.g	185.f	$4$	$2$	$1$	$2.954$	$\Q(\sqrt{-1}) $	None		✓			370.2.g.b	$2$	$0$	$0$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{2}-q^{4}+(i-2)q^{5}+(-2 i-2)q^{7}+\cdots$
370.2.g.c	$370$	$2$	370.g	185.f	$4$	$4$	$2$	$2.954$	$\Q(\zeta_{8})$	None		✓			370.2.g.c	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{2}q^{2}+2\zeta_{8}q^{3}-q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
370.2.g.d	$370$	$2$	370.g	185.f	$4$	$10$	$5$	$2.954$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓			370.2.g.d	$2$	$0$	$0$	$-2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{3}-\beta _{8})q^{3}-q^{4}+\cdots$
370.2.g.e	$370$	$2$	370.g	185.f	$4$	$20$	$10$	$2.954$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		370.2.g.e	$2$	$0$	$0$	$-4$	$2$	$-2$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{10}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{8}q^{5}+\beta _{4}q^{6}+\cdots$
370.2.h.a	$370$	$2$	370.h	185.k	$4$	$2$	$1$	$2.954$	$\Q(\sqrt{-1}) $	None		✓			370.2.g.b	$2$	$0$	$2$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+q^{4}+(2 i-1)q^{5}+(2 i-2)q^{7}+\cdots$
370.2.h.b	$370$	$2$	370.h	185.k	$4$	$2$	$1$	$2.954$	$\Q(\sqrt{-1}) $	None		✓			370.2.g.a	$2$	$0$	$2$	$2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(-i+1)q^{3}+q^{4}+(-2 i-1)q^{5}+\cdots$
370.2.h.c	$370$	$2$	370.h	185.k	$4$	$4$	$2$	$2.954$	$\Q(\zeta_{8})$	None		✓			370.2.g.c	$2$	$0$	$4$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+2\zeta_{8}q^{3}+q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots$
370.2.h.d	$370$	$2$	370.h	185.k	$4$	$10$	$5$	$2.954$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓			370.2.g.d	$2$	$0$	$10$	$2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
370.2.h.e	$370$	$2$	370.h	185.k	$4$	$20$	$10$	$2.954$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		370.2.g.e	$2$	$0$	$-20$	$4$	$-4$	$-2$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{13}q^{5}+\beta _{4}q^{6}+\cdots$
370.2.l.a	$370$	$2$	370.l	37.e	$6$	$4$	$2$	$2.954$	$\Q(\zeta_{12})$	None		✓			370.2.l.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
370.2.l.b	$370$	$2$	370.l	37.e	$6$	$4$	$2$	$2.954$	$\Q(\zeta_{12})$	None		✓			370.2.l.b	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
370.2.l.c	$370$	$2$	370.l	37.e	$6$	$12$	$6$	$2.954$	12.0.$\cdots$.2	None		✓	✓		370.2.l.c	$2$	$0$	$0$	$4$	$0$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{2}+(1-\beta _{6}+\beta _{10})q^{3}+(1-\beta _{6}+\cdots)q^{4}+\cdots$
370.2.m.a	$370$	$2$	370.m	185.l	$6$	$4$	$2$	$2.954$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			370.2.m.a	$2$	$1$	$-2$	$-3$	$-6$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
370.2.m.b	$370$	$2$	370.m	185.l	$6$	$4$	$2$	$2.954$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			370.2.m.a	$2$	$0$	$2$	$3$	$-3$	$12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{4}+\cdots$
370.2.m.c	$370$	$2$	370.m	185.l	$6$	$16$	$8$	$2.954$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			370.2.m.c	$2$	$0$	$-8$	$3$	$6$	$12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{1})q^{2}+\beta _{10}q^{3}+\beta _{1}q^{4}+\cdots$
370.2.m.d	$370$	$2$	370.m	185.l	$6$	$16$	$8$	$2.954$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			370.2.m.c	$2$	$0$	$8$	$-3$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{1})q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}+\beta _{8}q^{5}+\cdots$
370.2.n.a	$370$	$2$	370.n	185.n	$6$	$4$	$2$	$2.954$	$\Q(\zeta_{12})$	None		✓			370.2.n.a	$2$	$0$	$0$	$0$	$-8$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{3})q^{5}+\cdots$
370.2.n.b	$370$	$2$	370.n	185.n	$6$	$4$	$2$	$2.954$	$\Q(\zeta_{12})$	None		✓			370.2.n.b	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
370.2.n.c	$370$	$2$	370.n	185.n	$6$	$4$	$2$	$2.954$	$\Q(\zeta_{12})$	None		✓			370.2.n.a	$2$	$0$	$0$	$0$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
370.2.n.d	$370$	$2$	370.n	185.n	$6$	$4$	$2$	$2.954$	$\Q(\zeta_{12})$	None		✓			370.2.n.d	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
370.2.n.e	$370$	$2$	370.n	185.n	$6$	$8$	$4$	$2.954$	8.0.303595776.1	None		✓			370.2.n.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}-2\beta _{5}q^{3}-\beta _{4}q^{4}+(\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots$
370.2.n.f	$370$	$2$	370.n	185.n	$6$	$12$	$6$	$2.954$	12.0.$\cdots$.1	None		✓	✓		370.2.n.f	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(\beta _{5}-\beta _{6}-\beta _{7}+\beta _{9})q^{3}+\cdots$
370.2.o.a	$370$	$2$	370.o	37.f	$9$	$18$	$3$	$2.954$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓			370.2.o.a	$2$	$0$	$0$	$0$	$0$	$-3$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{8}-\beta _{17})q^{3}+\beta _{6}q^{4}+\cdots$
370.2.o.b	$370$	$2$	370.o	37.f	$9$	$18$	$3$	$2.954$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓			370.2.o.b	$2$	$0$	$0$	$0$	$0$	$-9$		$3^{2}$	$\mathrm{SU}(2)[C_{9}]$	$q+\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{10}+\beta _{11})q^{4}+\cdots$
370.2.o.c	$370$	$2$	370.o	37.f	$9$	$24$	$4$	$2.954$		None		✓			370.2.o.c	$2$	$0$	$0$	$0$	$0$	$-3$			$\mathrm{SU}(2)[C_{9}]$
370.2.o.d	$370$	$2$	370.o	37.f	$9$	$24$	$4$	$2.954$		None		✓			370.2.o.d	$2$	$0$	$0$	$0$	$0$	$-9$			$\mathrm{SU}(2)[C_{9}]$
370.2.q.a	$370$	$2$	370.q	185.p	$12$	$4$	$1$	$2.954$	$\Q(\zeta_{12})$	None		✓			370.2.q.a	$2$	$0$	$-2$	$4$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q-\zeta_{12}^{2}q^{2}+(1+\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$

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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.