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 135 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
190.2.a.a	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.b	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-3\)	\(-1\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots\)
190.2.a.c	$190$	$2$	190.a	1.a	$1$	$1$	$1$	$1.517$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.d	$190$	$2$	190.a	1.a	$1$	$2$	$2$	$1.517$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-2\)	\(-1\)	\(2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)
190.2.b.a	$190$	$2$	190.b	5.b	$2$	$4$	$4$	$1.517$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
190.2.b.b	$190$	$2$	190.b	5.b	$2$	$6$	$6$	$1.517$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
190.2.e.a	$190$	$2$	190.e	19.c	$3$	$2$	$1$	$1.517$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(1\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
190.2.e.b	$190$	$2$	190.e	19.c	$3$	$2$	$1$	$1.517$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(1\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
190.2.e.c	$190$	$2$	190.e	19.c	$3$	$4$	$2$	$1.517$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(2\)	\(1\)	\(-2\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
190.2.f.a	$190$	$2$	190.f	95.g	$4$	$4$	$2$	$1.517$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+2\zeta_{8}^{2})q^{5}+\cdots\)
190.2.f.b	$190$	$2$	190.f	95.g	$4$	$16$	$8$	$1.517$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{2}+(\beta _{1}-\beta _{7}+\beta _{10}+\beta _{12})q^{3}+\cdots\)
190.2.i.a	$190$	$2$	190.i	95.i	$6$	$20$	$10$	$1.517$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{13})q^{2}-\beta _{1}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
190.2.k.a	$190$	$2$	190.k	19.e	$9$	$6$	$1$	$1.517$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
190.2.k.b	$190$	$2$	190.k	19.e	$9$	$12$	$2$	$1.517$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
190.2.k.c	$190$	$2$	190.k	19.e	$9$	$12$	$2$	$1.517$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots\)
190.2.k.d	$190$	$2$	190.k	19.e	$9$	$18$	$3$	$1.517$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots\)
190.2.m.a	$190$	$2$	190.m	95.l	$12$	$8$	$2$	$1.517$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(12\)	\(4\)	\(-16\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}+(2+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
190.2.m.b	$190$	$2$	190.m	95.l	$12$	$32$	$8$	$1.517$		None		$4$	$0$	\(0\)	\(-12\)	\(0\)	\(24\)			$\mathrm{SU}(2)[C_{12}]$
190.2.p.a	$190$	$2$	190.p	95.p	$18$	$60$	$10$	$1.517$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
190.2.r.a	$190$	$2$	190.r	95.r	$36$	$120$	$10$	$1.517$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)			$\mathrm{SU}(2)[C_{36}]$
190.3.c.a	$190$	$3$	190.c	19.b	$2$	$16$	$16$	$5.177$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots\)
190.3.d.a	$190$	$3$	190.d	95.d	$2$	$20$	$20$	$5.177$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)
190.3.g.a	$190$	$3$	190.g	5.c	$4$	$16$	$8$	$5.177$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-16\)	\(8\)	\(2\)	\(-10\)		$2^{8}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{5})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots\)
190.3.g.b	$190$	$3$	190.g	5.c	$4$	$20$	$10$	$5.177$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(20\)	\(0\)	\(2\)	\(14\)		$2^{14}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{3})q^{2}-\beta _{2}q^{3}+2\beta _{3}q^{4}+\beta _{16}q^{5}+\cdots\)
190.3.h.a	$190$	$3$	190.h	95.h	$6$	$4$	$2$	$5.177$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
190.3.h.b	$190$	$3$	190.h	95.h	$6$	$36$	$18$	$5.177$		None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
190.3.j.a	$190$	$3$	190.j	19.d	$6$	$32$	$16$	$5.177$		None		$2$	$0$	\(0\)	\(-12\)	\(0\)	\(8\)			$\mathrm{SU}(2)[C_{6}]$
190.3.l.a	$190$	$3$	190.l	95.m	$12$	$4$	$1$	$5.177$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-2\)	\(-6\)	\(8\)	\(32\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+\cdots)q^{3}+\cdots\)
190.3.l.b	$190$	$3$	190.l	95.m	$12$	$4$	$1$	$5.177$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(6\)	\(10\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(3\zeta_{12}+\cdots)q^{3}+\cdots\)
190.3.l.c	$190$	$3$	190.l	95.m	$12$	$36$	$9$	$5.177$		None		$4$	$0$	\(-18\)	\(6\)	\(-10\)	\(-28\)			$\mathrm{SU}(2)[C_{12}]$
190.3.l.d	$190$	$3$	190.l	95.m	$12$	$36$	$9$	$5.177$		None		$4$	$0$	\(18\)	\(-6\)	\(-12\)	\(12\)			$\mathrm{SU}(2)[C_{12}]$
190.3.n.a	$190$	$3$	190.n	19.f	$18$	$72$	$12$	$5.177$		None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
190.3.o.a	$190$	$3$	190.o	95.o	$18$	$120$	$20$	$5.177$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
190.3.q.a	$190$	$3$	190.q	95.q	$36$	$120$	$10$	$5.177$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-18\)			$\mathrm{SU}(2)[C_{36}]$
190.3.q.b	$190$	$3$	190.q	95.q	$36$	$120$	$10$	$5.177$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-18\)			$\mathrm{SU}(2)[C_{36}]$
190.4.a.a	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(-2\)	\(5\)	\(8\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots\)
190.4.a.b	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(2\)	\(5\)	\(-12\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{3}+4q^{4}+5q^{5}-4q^{6}+\cdots\)
190.4.a.c	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(-4\)	\(5\)	\(-20\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots\)
190.4.a.d	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	\(\Q(\sqrt{313}) \)	None	✓	$1$	$0$	\(-4\)	\(1\)	\(10\)	\(-27\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots\)
190.4.a.e	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-4\)	\(2\)	\(-10\)	\(8\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1+3\beta )q^{3}+4q^{4}-5q^{5}+\cdots\)
190.4.a.f	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	\(\Q(\sqrt{34}) \)	None	✓	$1$	$0$	\(4\)	\(0\)	\(-10\)	\(24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots\)
190.4.a.g	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.126168.1	None	✓	$1$	$1$	\(-6\)	\(-1\)	\(-15\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots\)
190.4.a.h	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.5468.1	None	✓	$1$	$1$	\(6\)	\(-9\)	\(-15\)	\(-11\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
190.4.a.i	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.15357.1	None	✓	$1$	$0$	\(6\)	\(11\)	\(15\)	\(29\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
190.4.b.a	$190$	$4$	190.b	5.b	$2$	$12$	$12$	$11.210$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)		$2^{10}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}+(\beta _{8}-\beta _{9})q^{3}-4q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots\)
190.4.b.b	$190$	$4$	190.b	5.b	$2$	$14$	$14$	$11.210$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$2^{8}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}+\beta _{3}q^{3}-4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
190.4.e.a	$190$	$4$	190.e	19.c	$3$	$2$	$1$	$11.210$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(2\)	\(-5\)	\(-56\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
190.4.e.b	$190$	$4$	190.e	19.c	$3$	$2$	$1$	$11.210$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(2\)	\(5\)	\(64\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
190.4.e.c	$190$	$4$	190.e	19.c	$3$	$6$	$3$	$11.210$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(6\)	\(3\)	\(-15\)	\(36\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
190.4.e.d	$190$	$4$	190.e	19.c	$3$	$8$	$4$	$11.210$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(8\)	\(3\)	\(20\)	\(-82\)		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+2\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)