Newform search results

Level	Weight	Analytic conductor	\(Nk^2\)	Dim.
Bad \(p\)	Char.	Primitive character	Character order	Coefficient field
Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank
Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 162 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
570.2.a.a	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.b	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.c	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.d	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
570.2.a.e	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
570.2.a.f	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
570.2.a.g	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
570.2.a.h	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
570.2.a.i	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
570.2.a.j	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.k	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.l	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.m	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(1\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
570.2.c.a	$570$	$2$	570.c	285.b	$2$	$4$	$4$	$4.551$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.b	$570$	$2$	570.c	285.b	$2$	$4$	$4$	$4.551$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.c	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	8.0.1499238400.2	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.c.d	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
570.2.c.e	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots\)
570.2.c.f	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	8.0.1499238400.2	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.d.a	$570$	$2$	570.d	5.b	$2$	$2$	$2$	$4.551$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
570.2.d.b	$570$	$2$	570.d	5.b	$2$	$2$	$2$	$4.551$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
570.2.d.c	$570$	$2$	570.d	5.b	$2$	$6$	$6$	$4.551$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots\)
570.2.d.d	$570$	$2$	570.d	5.b	$2$	$6$	$6$	$4.551$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)
570.2.f.a	$570$	$2$	570.f	57.d	$2$	$4$	$4$	$4.551$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(8\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(-1-\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.b	$570$	$2$	570.f	57.d	$2$	$4$	$4$	$4.551$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(4\)	\(4\)	\(0\)	\(8\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(1+\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.c	$570$	$2$	570.f	57.d	$2$	$8$	$8$	$4.551$	8.0.7278137344.1	None		$2$	$0$	\(-8\)	\(2\)	\(0\)	\(4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.f.d	$570$	$2$	570.f	57.d	$2$	$8$	$8$	$4.551$	8.0.7278137344.1	None		$2$	$0$	\(8\)	\(-2\)	\(0\)	\(4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.i.a	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.b	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.c	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(1\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.d	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-1\)	\(1\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.e	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(-1\)	\(-10\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.f	$570$	$2$	570.i	19.c	$3$	$4$	$2$	$4.551$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(-2\)	\(2\)	\(-2\)	\(4\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.i.g	$570$	$2$	570.i	19.c	$3$	$4$	$2$	$4.551$	\(\Q(\sqrt{-3}, \sqrt{73})\)	None		$2$	$0$	\(2\)	\(-2\)	\(-2\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
570.2.i.h	$570$	$2$	570.i	19.c	$3$	$4$	$2$	$4.551$	\(\Q(\sqrt{-3}, \sqrt{19})\)	None		$2$	$0$	\(2\)	\(-2\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.i	$570$	$2$	570.i	19.c	$3$	$4$	$2$	$4.551$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(2\)	\(2\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.j	$570$	$2$	570.i	19.c	$3$	$6$	$3$	$4.551$	6.0.29654208.1	None		$2$	$0$	\(-3\)	\(-3\)	\(-3\)	\(2\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.k.a	$570$	$2$	570.k	15.e	$4$	$36$	$18$	$4.551$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-12\)			$\mathrm{SU}(2)[C_{4}]$
570.2.k.b	$570$	$2$	570.k	15.e	$4$	$36$	$18$	$4.551$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(20\)			$\mathrm{SU}(2)[C_{4}]$
570.2.m.a	$570$	$2$	570.m	95.g	$4$	$20$	$10$	$4.551$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\)
570.2.m.b	$570$	$2$	570.m	95.g	$4$	$20$	$10$	$4.551$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(-4\)		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
570.2.n.a	$570$	$2$	570.n	285.q	$6$	$80$	$40$	$4.551$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
570.2.q.a	$570$	$2$	570.q	95.i	$6$	$8$	$4$	$4.551$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{3}+\cdots\)
570.2.q.b	$570$	$2$	570.q	95.i	$6$	$12$	$6$	$4.551$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+\cdots\)
570.2.q.c	$570$	$2$	570.q	95.i	$6$	$20$	$10$	$4.551$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}+\beta _{11}q^{3}+(1-\beta _{12})q^{4}+\cdots\)
570.2.s.a	$570$	$2$	570.s	57.f	$6$	$24$	$12$	$4.551$		None		$2$	$0$	\(-12\)	\(4\)	\(0\)	\(-12\)			$\mathrm{SU}(2)[C_{6}]$
570.2.s.b	$570$	$2$	570.s	57.f	$6$	$24$	$12$	$4.551$		None		$2$	$0$	\(12\)	\(2\)	\(0\)	\(-12\)			$\mathrm{SU}(2)[C_{6}]$
570.2.u.a	$570$	$2$	570.u	19.e	$9$	$6$	$1$	$4.551$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.b	$570$	$2$	570.u	19.e	$9$	$6$	$1$	$4.551$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.c	$570$	$2$	570.u	19.e	$9$	$6$	$1$	$4.551$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)