Newform search results

Results (1-50 of 2077 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.2.e.a	$27$	$2$	27.e	27.e	$9$	$12$	$2$	$0.216$	12.0.\(\cdots\).1	None		$2$	$0$	\(-6\)	\(-6\)	\(-3\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)
29.2.e.a	$29$	$2$	29.e	29.e	$14$	$12$	$2$	$0.232$	12.0.\(\cdots\).1	None		$2$	$0$	\(-7\)	\(-7\)	\(-1\)	\(-11\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)
31.2.g.a	$31$	$2$	31.g	31.g	$15$	$16$	$2$	$0.248$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-6\)	\(-12\)	\(-3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
37.2.h.a	$37$	$2$	37.h	37.h	$18$	$18$	$3$	$0.295$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-9\)	\(-9\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(\beta _{4}-\beta _{11})q^{2}+(-1-\beta _{12}+\beta _{16}+\cdots)q^{3}+\cdots\)
44.2.g.a	$44$	$2$	44.g	44.g	$10$	$16$	$4$	$0.351$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-5\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots\)
45.2.l.a	$45$	$2$	45.l	45.l	$12$	$16$	$4$	$0.359$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-6\)	\(-6\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{5}q^{2}+(-1+\beta _{9}-\beta _{11}-\beta _{12}+\cdots)q^{3}+\cdots\)
48.2.k.a	$48$	$2$	48.k	48.k	$4$	$12$	$6$	$0.383$	12.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{2}-\beta _{10}q^{3}+(-\beta _{1}+\beta _{10}+\beta _{11})q^{4}+\cdots\)
49.2.e.b	$49$	$2$	49.e	49.e	$7$	$12$	$2$	$0.391$	\(\Q(\zeta_{21})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-7\)	\(-7\)	$7$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\zeta_{21}^{2}+\zeta_{21}^{4}-\zeta_{21}^{5}-\zeta_{21}^{9}+\zeta_{21}^{11})q^{2}+\cdots\)
52.2.l.b	$52$	$2$	52.l	52.l	$12$	$16$	$4$	$0.415$	16.0.\(\cdots\).1	None		$4$	$0$	\(-2\)	\(0\)	\(-12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{12}q^{2}+(\beta _{3}+\beta _{12}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
54.2.e.b	$54$	$2$	54.e	27.e	$9$	$12$	$2$	$0.431$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{11}q^{3}+\beta _{3}q^{4}+\cdots\)
55.2.j.a	$55$	$2$	55.j	55.j	$10$	$16$	$4$	$0.439$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots\)
56.2.m.a	$56$	$2$	56.m	56.m	$6$	$12$	$6$	$0.447$	12.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{8})q^{2}+(-1-\beta _{10})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
56.2.p.a	$56$	$2$	56.p	56.p	$6$	$12$	$6$	$0.447$	12.0.\(\cdots\).1	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots\)
57.2.i.b	$57$	$2$	57.i	19.e	$9$	$12$	$2$	$0.455$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(6\)	\(-9\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{6}q^{3}+\cdots\)
58.2.d.b	$58$	$2$	58.d	29.d	$7$	$12$	$2$	$0.463$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-3\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{6}q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
58.2.e.a	$58$	$2$	58.e	29.e	$14$	$12$	$2$	$0.463$	\(\Q(\zeta_{28})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q-\zeta_{28}^{9}q^{2}+(-\zeta_{28}-\zeta_{28}^{3}-\zeta_{28}^{5}+\cdots)q^{3}+\cdots\)
60.2.j.a	$60$	$2$	60.j	20.e	$4$	$12$	$6$	$0.479$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{2}+\beta _{4}-\beta _{7})q^{4}+\cdots\)
61.2.e.a	$61$	$2$	61.e	61.e	$5$	$12$	$3$	$0.487$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-1\)	\(-5\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{5}q^{2}+(\beta _{8}+\beta _{10})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
61.2.g.a	$61$	$2$	61.g	61.g	$10$	$16$	$4$	$0.487$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-5\)	\(-1\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{1}+\beta _{2}-2\beta _{4}-2\beta _{5}+\cdots)q^{3}+\cdots\)
63.2.o.a	$63$	$2$	63.o	63.o	$6$	$12$	$6$	$0.503$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{4}+\beta _{7})q^{4}+\cdots\)
19.3.f.a	$19$	$3$	19.f	19.f	$18$	$12$	$2$	$0.518$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-6\)	\(0\)	\(-6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\beta _{10}q^{2}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)
65.2.n.a	$65$	$2$	65.n	65.n	$6$	$12$	$6$	$0.519$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}+(\beta _{4}-\beta _{11})q^{3}+(-\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots\)
65.2.o.a	$65$	$2$	65.o	65.o	$12$	$20$	$5$	$0.519$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-4\)	\(-2\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}+\cdots)q^{3}+\cdots\)
65.2.t.a	$65$	$2$	65.t	65.t	$12$	$20$	$5$	$0.519$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-6\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
67.2.e.c	$67$	$2$	67.e	67.e	$11$	$20$	$2$	$0.535$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-4\)	\(-4\)	\(1\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\beta _{9}-\beta _{14})q^{2}-\beta _{19}q^{3}+(-1+\cdots)q^{4}+\cdots\)
69.2.e.c	$69$	$2$	69.e	23.c	$11$	$20$	$2$	$0.551$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-4\)	\(-2\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+2\beta _{6}+2\beta _{7}+\cdots)q^{2}+\cdots\)
70.2.k.a	$70$	$2$	70.k	35.k	$12$	$16$	$4$	$0.559$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{7}-\beta _{15})q^{2}+(-\beta _{4}+\beta _{13})q^{3}+\cdots\)
71.2.c.a	$71$	$2$	71.c	71.c	$5$	$20$	$5$	$0.567$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-6\)	\(-1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{14}q^{2}+\beta _{17}q^{3}+(-\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
72.2.l.b	$72$	$2$	72.l	72.l	$6$	$16$	$8$	$0.575$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-3\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
72.2.n.b	$72$	$2$	72.n	72.n	$6$	$16$	$8$	$0.575$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(6\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots\)
73.2.h.a	$73$	$2$	73.h	73.h	$12$	$20$	$5$	$0.583$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{9}q^{2}+(\beta _{2}+\beta _{6}-\beta _{8}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)
74.2.f.b	$74$	$2$	74.f	37.f	$9$	$12$	$2$	$0.591$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-3\)	\(-6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{4}-\beta _{7})q^{2}+(-1+\beta _{1}-\beta _{8})q^{3}+\cdots\)
74.2.h.a	$74$	$2$	74.h	37.h	$18$	$12$	$2$	$0.591$	\(\Q(\zeta_{36})\)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\zeta_{36}q^{2}+(1-\zeta_{36}^{4}-\zeta_{36}^{6})q^{3}+\cdots\)
75.2.g.c	$75$	$2$	75.g	25.d	$5$	$12$	$3$	$0.599$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(3\)	\(-6\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+\beta _{8}q^{3}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots\)
75.2.i.a	$75$	$2$	75.i	25.e	$10$	$16$	$4$	$0.599$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\beta _{2}-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{2}+\cdots\)
76.2.f.a	$76$	$2$	76.f	76.f	$6$	$16$	$8$	$0.607$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-3\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots\)
76.2.i.a	$76$	$2$	76.i	19.e	$9$	$12$	$2$	$0.607$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots\)
77.2.f.b	$77$	$2$	77.f	11.c	$5$	$16$	$4$	$0.615$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-3\)	\(-2\)	\(-5\)	\(-4\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{5}-\beta _{6})q^{2}+(\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)
77.2.i.a	$77$	$2$	77.i	77.i	$6$	$12$	$6$	$0.615$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{7})q^{2}+(-1+\beta _{2}-\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots\)
77.2.l.b	$77$	$2$	77.l	77.l	$10$	$16$	$4$	$0.615$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(-10\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
78.2.g.a	$78$	$2$	78.g	39.f	$4$	$12$	$6$	$0.623$	12.0.\(\cdots\).52	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}-\beta _{4}q^{3}+\beta _{8}q^{4}+(-\beta _{1}-\beta _{11})q^{5}+\cdots\)
78.2.k.a	$78$	$2$	78.k	39.k	$12$	$16$	$4$	$0.623$	16.0.\(\cdots\).9	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{7}-\beta _{15})q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
79.2.c.a	$79$	$2$	79.c	79.c	$3$	$12$	$6$	$0.631$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots\)
80.2.j.b	$80$	$2$	80.j	80.j	$4$	$18$	$9$	$0.639$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(2\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{2}-\beta _{16}q^{3}-\beta _{13}q^{4}+(-1+\cdots)q^{5}+\cdots\)
80.2.l.a	$80$	$2$	80.l	16.e	$4$	$16$	$8$	$0.639$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{9}q^{2}+(\beta _{3}-\beta _{6}+\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
80.2.q.c	$80$	$2$	80.q	80.q	$4$	$16$	$8$	$0.639$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{12}q^{2}+(-\beta _{3}-\beta _{11}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
80.2.s.b	$80$	$2$	80.s	80.s	$4$	$18$	$9$	$0.639$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots\)
81.2.e.a	$81$	$2$	81.e	27.e	$9$	$12$	$2$	$0.647$	12.0.\(\cdots\).1	None		$2$	$0$	\(6\)	\(0\)	\(3\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1+\beta _{3}-\beta _{8})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
82.2.g.b	$82$	$2$	82.g	41.g	$20$	$16$	$2$	$0.655$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{20}]$	\(q-\beta _{12}q^{2}+(-2+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{7}+\cdots)q^{3}+\cdots\)
84.2.e.a	$84$	$2$	84.e	12.b	$2$	$12$	$12$	$0.671$	12.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-\beta _{9}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\)