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 214 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
270.2.a.a	$270$	$2$	270.a	1.a	$1$	$1$	$1$	$2.156$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
270.2.a.b	$270$	$2$	270.a	1.a	$1$	$1$	$1$	$2.156$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
270.2.a.c	$270$	$2$	270.a	1.a	$1$	$1$	$1$	$2.156$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
270.2.a.d	$270$	$2$	270.a	1.a	$1$	$1$	$1$	$2.156$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
270.2.c.a	$270$	$2$	270.c	5.b	$2$	$2$	$2$	$2.156$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-1-2i)q^{5}-4iq^{7}+\cdots\)
270.2.c.b	$270$	$2$	270.c	5.b	$2$	$2$	$2$	$2.156$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots\)
270.2.c.c	$270$	$2$	270.c	5.b	$2$	$4$	$4$	$2.156$	\(\Q(i, \sqrt{19})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+(1+2\beta _{3})q^{7}+\cdots\)
270.2.e.a	$270$	$2$	270.e	9.c	$3$	$2$	$1$	$2.156$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(1\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
270.2.e.b	$270$	$2$	270.e	9.c	$3$	$2$	$1$	$2.156$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
270.2.e.c	$270$	$2$	270.e	9.c	$3$	$4$	$2$	$2.156$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(-1\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
270.2.f.a	$270$	$2$	270.f	15.e	$4$	$8$	$4$	$2.156$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
270.2.f.b	$270$	$2$	270.f	15.e	$4$	$8$	$4$	$2.156$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{24}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{6}q^{4}+(2\zeta_{24}+\cdots)q^{5}+\cdots\)
270.2.i.a	$270$	$2$	270.i	45.j	$6$	$4$	$2$	$2.156$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
270.2.i.b	$270$	$2$	270.i	45.j	$6$	$8$	$4$	$2.156$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)
270.2.k.a	$270$	$2$	270.k	27.e	$9$	$6$	$1$	$2.156$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}-2\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
270.2.k.b	$270$	$2$	270.k	27.e	$9$	$12$	$2$	$2.156$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(-12\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{7}q^{2}+(1-\beta _{5}-\beta _{7}-\beta _{11})q^{3}+\cdots\)
270.2.k.c	$270$	$2$	270.k	27.e	$9$	$12$	$2$	$2.156$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(6\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{7}-\beta _{10})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots\)
270.2.k.d	$270$	$2$	270.k	27.e	$9$	$18$	$3$	$2.156$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-3\)		$3^{3}$	$\mathrm{SU}(2)[C_{9}]$	\(q+\beta _{2}q^{2}-\beta _{7}q^{3}+\beta _{3}q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots\)
270.2.k.e	$270$	$2$	270.k	27.e	$9$	$24$	$4$	$2.156$		None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(3\)			$\mathrm{SU}(2)[C_{9}]$
270.2.m.a	$270$	$2$	270.m	45.l	$12$	$8$	$2$	$2.156$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
270.2.m.b	$270$	$2$	270.m	45.l	$12$	$16$	$4$	$2.156$	16.0.\(\cdots\).9	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{5}q^{2}-\beta _{6}q^{4}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
270.2.p.a	$270$	$2$	270.p	135.p	$18$	$108$	$18$	$2.156$		None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
270.2.r.a	$270$	$2$	270.r	135.q	$36$	$216$	$18$	$2.156$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{36}]$
270.3.b.a	$270$	$3$	270.b	15.d	$2$	$4$	$4$	$7.357$	4.0.31744.1	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+2q^{4}+(-3-\beta _{1}-\beta _{2})q^{5}+\cdots\)
270.3.b.b	$270$	$3$	270.b	15.d	$2$	$4$	$4$	$7.357$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(3\zeta_{8}-4\zeta_{8}^{3})q^{5}+\cdots\)
270.3.b.c	$270$	$3$	270.b	15.d	$2$	$4$	$4$	$7.357$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}+5\zeta_{8}^{2}q^{7}+\cdots\)
270.3.b.d	$270$	$3$	270.b	15.d	$2$	$4$	$4$	$7.357$	4.0.31744.1	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+2q^{4}+(3-\beta _{1}+\beta _{2})q^{5}+\cdots\)
270.3.d.a	$270$	$3$	270.d	3.b	$2$	$4$	$4$	$7.357$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-q^{7}+2\beta _{1}q^{8}+\cdots\)
270.3.d.b	$270$	$3$	270.d	3.b	$2$	$8$	$8$	$7.357$	8.0.40960000.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{6}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-2q^{4}-\beta _{1}q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots\)
270.3.g.a	$270$	$3$	270.g	5.c	$4$	$4$	$2$	$7.357$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(-4\)	\(0\)	\(-12\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}+2\beta _{2}q^{4}+(-3-2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.b	$270$	$3$	270.g	5.c	$4$	$4$	$2$	$7.357$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(-4\)	\(0\)	\(12\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.c	$270$	$3$	270.g	5.c	$4$	$4$	$2$	$7.357$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(4\)	\(0\)	\(-12\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}+(-3+2\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.d	$270$	$3$	270.g	5.c	$4$	$4$	$2$	$7.357$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(4\)	\(0\)	\(12\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
270.3.g.e	$270$	$3$	270.g	5.c	$4$	$8$	$4$	$7.357$	8.0.\(\cdots\).38	None		$2$	$0$	\(-8\)	\(0\)	\(12\)	\(-8\)		$3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.g.f	$270$	$3$	270.g	5.c	$4$	$8$	$4$	$7.357$	8.0.\(\cdots\).38	None		$2$	$0$	\(8\)	\(0\)	\(-12\)	\(-8\)		$3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
270.3.h.a	$270$	$3$	270.h	9.d	$6$	$16$	$8$	$7.357$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}-2\beta _{10}q^{4}+\beta _{12}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
270.3.j.a	$270$	$3$	270.j	45.h	$6$	$8$	$4$	$7.357$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots\)
270.3.j.b	$270$	$3$	270.j	45.h	$6$	$16$	$8$	$7.357$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-30\)	\(0\)		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-2-2\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
270.3.l.a	$270$	$3$	270.l	45.k	$12$	$24$	$6$	$7.357$		None		$4$	$0$	\(-12\)	\(0\)	\(0\)	\(6\)			$\mathrm{SU}(2)[C_{12}]$
270.3.l.b	$270$	$3$	270.l	45.k	$12$	$24$	$6$	$7.357$		None		$4$	$0$	\(12\)	\(0\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{12}]$
270.3.n.a	$270$	$3$	270.n	135.n	$18$	$216$	$36$	$7.357$		None		$4$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
270.3.o.a	$270$	$3$	270.o	27.f	$18$	$144$	$24$	$7.357$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
270.3.q.a	$270$	$3$	270.q	135.r	$36$	$216$	$18$	$7.357$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(18\)			$\mathrm{SU}(2)[C_{36}]$
270.3.q.b	$270$	$3$	270.q	135.r	$36$	$216$	$18$	$7.357$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-18\)			$\mathrm{SU}(2)[C_{36}]$
270.4.a.a	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-5\)	\(-34\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}-5q^{5}-34q^{7}-8q^{8}+\cdots\)
270.4.a.b	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-5\)	\(8\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}-5q^{5}+8q^{7}-8q^{8}+\cdots\)
270.4.a.c	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(5\)	\(-22\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+5q^{5}-22q^{7}-8q^{8}+\cdots\)
270.4.a.d	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(5\)	\(-13\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+5q^{5}-13q^{7}-8q^{8}+\cdots\)
270.4.a.e	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(5\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots\)
270.4.a.f	$270$	$4$	270.a	1.a	$1$	$1$	$1$	$15.931$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(5\)	\(14\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+5q^{5}+14q^{7}-8q^{8}+\cdots\)