Newform search results

Results (1-50 of 76 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
67.2.a.a	$67$	$2$	67.a	1.a	$1$	$1$	$1$	$0.535$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-2\)	\(2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+2q^{4}+2q^{5}-4q^{6}+\cdots\)
67.2.a.b	$67$	$2$	67.a	1.a	$1$	$2$	$2$	$0.535$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-3\)	\(-6\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
67.2.a.c	$67$	$2$	67.a	1.a	$1$	$2$	$2$	$0.535$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(4\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
67.2.c.a	$67$	$2$	67.c	67.c	$3$	$10$	$5$	$0.535$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(2\)	\(-8\)	\(-6\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
67.2.e.a	$67$	$2$	67.e	67.e	$11$	$10$	$1$	$0.535$	\(\Q(\zeta_{22})\)	None		$2$	$0$	\(-6\)	\(-2\)	\(3\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1-\zeta_{22}^{2}-\zeta_{22}^{4}+\zeta_{22}^{7}-\zeta_{22}^{8}+\cdots)q^{2}+\cdots\)
67.2.e.b	$67$	$2$	67.e	67.e	$11$	$10$	$1$	$0.535$	\(\Q(\zeta_{22})\)	None		$2$	$0$	\(4\)	\(3\)	\(-9\)	\(7\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\zeta_{22}+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}+\cdots)q^{2}+\cdots\)
67.2.e.c	$67$	$2$	67.e	67.e	$11$	$20$	$2$	$0.535$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-4\)	\(-4\)	\(1\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\beta _{9}-\beta _{14})q^{2}-\beta _{19}q^{3}+(-1+\cdots)q^{4}+\cdots\)
67.2.g.a	$67$	$2$	67.g	67.g	$33$	$100$	$5$	$0.535$		None		$2$	$0$	\(-24\)	\(-14\)	\(-16\)	\(-24\)			$\mathrm{SU}(2)[C_{33}]$
67.3.b.a	$67$	$3$	67.b	67.b	$2$	$1$	$1$	$1.826$	\(\Q\)	\(\Q(\sqrt{-67}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+9q^{9}+2^{4}q^{16}-33q^{17}+\cdots\)
67.3.b.b	$67$	$3$	67.b	67.b	$2$	$10$	$10$	$1.826$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$7$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
67.3.d.a	$67$	$3$	67.d	67.d	$6$	$20$	$10$	$1.826$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-12\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-\beta _{6}+\beta _{9})q^{3}+(-\beta _{1}+\beta _{11}+\cdots)q^{4}+\cdots\)
67.3.f.a	$67$	$3$	67.f	67.f	$22$	$110$	$11$	$1.826$		None		$2$	$0$	\(-11\)	\(-11\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
67.3.h.a	$67$	$3$	67.h	67.h	$66$	$200$	$10$	$1.826$		None		$2$	$0$	\(-19\)	\(-22\)	\(-22\)	\(-10\)			$\mathrm{SU}(2)[C_{66}]$
67.4.a.a	$67$	$4$	67.a	1.a	$1$	$7$	$7$	$3.953$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(-9\)	\(-45\)	\(-32\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{4})q^{3}+\cdots\)
67.4.a.b	$67$	$4$	67.a	1.a	$1$	$9$	$9$	$3.953$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(9\)	\(45\)	\(24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{7})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
67.4.c.a	$67$	$4$	67.c	67.c	$3$	$32$	$16$	$3.953$		None		$2$	$0$	\(-5\)	\(18\)	\(24\)	\(11\)			$\mathrm{SU}(2)[C_{3}]$
67.4.e.a	$67$	$4$	67.e	67.e	$11$	$160$	$16$	$3.953$		None		$2$	$0$	\(-13\)	\(-11\)	\(-11\)	\(-3\)			$\mathrm{SU}(2)[C_{11}]$
67.4.g.a	$67$	$4$	67.g	67.g	$33$	$320$	$16$	$3.953$		None		$2$	$0$	\(-17\)	\(-40\)	\(-46\)	\(-33\)			$\mathrm{SU}(2)[C_{33}]$
67.5.b.a	$67$	$5$	67.b	67.b	$2$	$1$	$1$	$6.926$	\(\Q\)	\(\Q(\sqrt{-67}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{4}+3^{4}q^{9}+2^{8}q^{16}+511q^{17}+\cdots\)
67.5.b.b	$67$	$5$	67.b	67.b	$2$	$20$	$20$	$6.926$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-8+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots\)
67.5.d.a	$67$	$5$	67.d	67.d	$6$	$44$	$22$	$6.926$		None		$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{6}]$
67.5.f.a	$67$	$5$	67.f	67.f	$22$	$210$	$21$	$6.926$		None		$2$	$0$	\(-11\)	\(-11\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
67.5.h.a	$67$	$5$	67.h	67.h	$66$	$440$	$22$	$6.926$		None		$2$	$0$	\(-19\)	\(-22\)	\(-22\)	\(-16\)			$\mathrm{SU}(2)[C_{66}]$
67.6.a.a	$67$	$6$	67.a	1.a	$1$	$13$	$13$	$10.746$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(-16\)	\(-27\)	\(-222\)	\(-293\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-2-\beta _{7})q^{3}+(15+\cdots)q^{4}+\cdots\)
67.6.a.b	$67$	$6$	67.a	1.a	$1$	$15$	$15$	$10.746$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(12\)	\(27\)	\(228\)	\(99\)	$-$	$2^{2}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{5})q^{3}+(19-\beta _{1}+\cdots)q^{4}+\cdots\)
67.6.c.a	$67$	$6$	67.c	67.c	$3$	$54$	$27$	$10.746$		None		$2$	$0$	\(1\)	\(-48\)	\(-162\)	\(-74\)			$\mathrm{SU}(2)[C_{3}]$
67.6.e.a	$67$	$6$	67.e	67.e	$11$	$280$	$28$	$10.746$		None		$2$	$0$	\(-7\)	\(-11\)	\(-17\)	\(183\)			$\mathrm{SU}(2)[C_{11}]$
67.6.g.a	$67$	$6$	67.g	67.g	$33$	$540$	$27$	$10.746$		None		$2$	$0$	\(-23\)	\(26\)	\(140\)	\(52\)			$\mathrm{SU}(2)[C_{33}]$
67.7.b.a	$67$	$7$	67.b	67.b	$2$	$1$	$1$	$15.414$	\(\Q\)	\(\Q(\sqrt{-67}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{6}q^{4}+3^{6}q^{9}+2^{12}q^{16}-7326q^{17}+\cdots\)
67.7.b.b	$67$	$7$	67.b	67.b	$2$	$32$	$32$	$15.414$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
67.7.d.a	$67$	$7$	67.d	67.d	$6$	$66$	$33$	$15.414$		None		$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-843\)			$\mathrm{SU}(2)[C_{6}]$
67.7.f.a	$67$	$7$	67.f	67.f	$22$	$330$	$33$	$15.414$		None		$2$	$0$	\(-11\)	\(-11\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
67.7.h.a	$67$	$7$	67.h	67.h	$66$	$660$	$33$	$15.414$		None		$2$	$0$	\(-19\)	\(-22\)	\(-22\)	\(821\)			$\mathrm{SU}(2)[C_{66}]$
67.8.a.a	$67$	$8$	67.a	1.a	$1$	$18$	$18$	$20.930$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$1$	\(-32\)	\(-81\)	\(-930\)	\(-501\)	$-$	$2^{9}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(-4+\beta _{6})q^{3}+(59+\cdots)q^{4}+\cdots\)
67.8.a.b	$67$	$8$	67.a	1.a	$1$	$20$	$20$	$20.930$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$0$	\(24\)	\(81\)	\(1320\)	\(2243\)	$+$	$2^{9}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(4-\beta _{3})q^{3}+(68+2\beta _{1}+\cdots)q^{4}+\cdots\)
67.8.c.a	$67$	$8$	67.c	67.c	$3$	$78$	$39$	$20.930$		None		$2$	$0$	\(5\)	\(24\)	\(354\)	\(-2170\)			$\mathrm{SU}(2)[C_{3}]$
67.8.e.a	$67$	$8$	67.e	67.e	$11$	$380$	$38$	$20.930$		None		$2$	$0$	\(-3\)	\(-11\)	\(-401\)	\(-1753\)			$\mathrm{SU}(2)[C_{11}]$
67.8.g.a	$67$	$8$	67.g	67.g	$33$	$780$	$39$	$20.930$		None		$2$	$0$	\(-27\)	\(-46\)	\(-376\)	\(2148\)			$\mathrm{SU}(2)[C_{33}]$
67.9.b.a	$67$	$9$	67.b	67.b	$2$	$1$	$1$	$27.294$	\(\Q\)	\(\Q(\sqrt{-67}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{4}+3^{8}q^{9}+2^{16}q^{16}+94079q^{17}+\cdots\)
67.9.b.b	$67$	$9$	67.b	67.b	$2$	$44$	$44$	$27.294$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
67.9.d.a	$67$	$9$	67.d	67.d	$6$	$88$	$44$	$27.294$		None		$2$	$0$	\(-3\)	\(0\)	\(0\)	\(2424\)			$\mathrm{SU}(2)[C_{6}]$
67.9.f.a	$67$	$9$	67.f	67.f	$22$	$450$	$45$	$27.294$		None		$2$	$0$	\(-11\)	\(-11\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
67.9.h.a	$67$	$9$	67.h	67.h	$66$	$880$	$44$	$27.294$		None		$2$	$0$	\(-19\)	\(-22\)	\(-22\)	\(-2446\)			$\mathrm{SU}(2)[C_{66}]$
67.10.a.a	$67$	$10$	67.a	1.a	$1$	$24$	$24$	$34.507$		None	✓	$1$	$1$	\(-48\)	\(-243\)	\(-7047\)	\(-12576\)	$+$		$\mathrm{SU}(2)$
67.10.a.b	$67$	$10$	67.a	1.a	$1$	$26$	$26$	$34.507$		None	✓	$1$	$0$	\(64\)	\(243\)	\(4203\)	\(6632\)	$-$		$\mathrm{SU}(2)$
67.10.c.a	$67$	$10$	67.c	67.c	$3$	$100$	$50$	$34.507$		None		$2$	$0$	\(-19\)	\(114\)	\(-912\)	\(6283\)			$\mathrm{SU}(2)[C_{3}]$
67.10.e.a	$67$	$10$	67.e	67.e	$11$	$500$	$50$	$34.507$		None		$2$	$0$	\(-27\)	\(-11\)	\(2833\)	\(5933\)			$\mathrm{SU}(2)[C_{11}]$
67.10.g.a	$67$	$10$	67.g	67.g	$33$	$1000$	$50$	$34.507$		None		$2$	$0$	\(-3\)	\(-136\)	\(890\)	\(-6305\)			$\mathrm{SU}(2)[C_{33}]$
67.11.b.a	$67$	$11$	67.b	67.b	$2$	$1$	$1$	$42.569$	\(\Q\)	\(\Q(\sqrt{-67}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{10}q^{4}+3^{10}q^{9}+2^{20}q^{16}-987393q^{17}+\cdots\)
67.11.b.b	$67$	$11$	67.b	67.b	$2$	$54$	$54$	$42.569$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$