Newform search results

Results (1-50 of 91 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
61.2.a.a	$61$	$2$	61.a	1.a	$1$	$1$	$1$	$0.487$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-3\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots\)
61.2.a.b	$61$	$2$	61.a	1.a	$1$	$3$	$3$	$0.487$	3.3.148.1	None	✓	$1$	$0$	\(1\)	\(2\)	\(-1\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
61.2.b.a	$61$	$2$	61.b	61.b	$2$	$4$	$4$	$0.487$	4.0.29952.1	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
61.2.c.a	$61$	$2$	61.c	61.c	$3$	$8$	$4$	$0.487$	8.0.310217769.2	None		$2$	$0$	\(0\)	\(-6\)	\(-2\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
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.f.a	$61$	$2$	61.f	61.f	$6$	$2$	$1$	$0.487$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-4\)	\(-3\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}-2q^{3}+\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots\)
61.2.f.b	$61$	$2$	61.f	61.f	$6$	$8$	$4$	$0.487$	8.0.542936601.2	None		$2$	$0$	\(0\)	\(-2\)	\(6\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{6})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
61.2.g.a	$61$	$2$	61.g	61.g	$10$	$16$	$4$	$0.487$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-5\)	\(-1\)	\(0\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{1}+\beta _{2}-2\beta _{4}-2\beta _{5}+\cdots)q^{3}+\cdots\)
61.2.i.a	$61$	$2$	61.i	61.i	$15$	$32$	$4$	$0.487$		None		$2$	$0$	\(-10\)	\(-4\)	\(2\)	\(1\)			$\mathrm{SU}(2)[C_{15}]$
61.2.k.a	$61$	$2$	61.k	61.k	$30$	$40$	$5$	$0.487$		None		$2$	$0$	\(-7\)	\(-4\)	\(-18\)	\(-11\)			$\mathrm{SU}(2)[C_{30}]$
61.3.d.a	$61$	$3$	61.d	61.d	$4$	$20$	$10$	$1.662$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(2\)		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+\beta _{12}q^{3}+(2\beta _{11}+\beta _{15})q^{4}+\cdots\)
61.3.h.a	$61$	$3$	61.h	61.h	$12$	$36$	$9$	$1.662$		None		$2$	$0$	\(-2\)	\(0\)	\(6\)	\(-18\)			$\mathrm{SU}(2)[C_{12}]$
61.3.j.a	$61$	$3$	61.j	61.j	$20$	$80$	$10$	$1.662$		None		$2$	$0$	\(-6\)	\(-10\)	\(-30\)	\(-12\)			$\mathrm{SU}(2)[C_{20}]$
61.3.l.a	$61$	$3$	61.l	61.l	$60$	$144$	$9$	$1.662$		None		$2$	$0$	\(-18\)	\(-20\)	\(-6\)	\(-2\)			$\mathrm{SU}(2)[C_{60}]$
61.4.a.a	$61$	$4$	61.a	1.a	$1$	$6$	$6$	$3.599$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(-13\)	\(-16\)	\(-27\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{4})q^{3}+\cdots\)
61.4.a.b	$61$	$4$	61.a	1.a	$1$	$9$	$9$	$3.599$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(11\)	\(24\)	\(1\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(6+\beta _{2})q^{4}+\cdots\)
61.4.b.a	$61$	$4$	61.b	61.b	$2$	$14$	$14$	$3.599$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(-14\)	\(0\)		$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
61.4.c.a	$61$	$4$	61.c	61.c	$3$	$30$	$15$	$3.599$		None		$2$	$0$	\(1\)	\(8\)	\(-11\)	\(23\)			$\mathrm{SU}(2)[C_{3}]$
61.4.e.a	$61$	$4$	61.e	61.e	$5$	$60$	$15$	$3.599$		None		$2$	$0$	\(-1\)	\(-3\)	\(-33\)	\(-29\)			$\mathrm{SU}(2)[C_{5}]$
61.4.f.a	$61$	$4$	61.f	61.f	$6$	$28$	$14$	$3.599$		None		$2$	$0$	\(-3\)	\(8\)	\(-22\)	\(33\)			$\mathrm{SU}(2)[C_{6}]$
61.4.g.a	$61$	$4$	61.g	61.g	$10$	$56$	$14$	$3.599$		None		$2$	$0$	\(-5\)	\(-3\)	\(-26\)	\(45\)			$\mathrm{SU}(2)[C_{10}]$
61.4.i.a	$61$	$4$	61.i	61.i	$15$	$120$	$15$	$3.599$		None		$2$	$0$	\(-11\)	\(-18\)	\(21\)	\(-73\)			$\mathrm{SU}(2)[C_{15}]$
61.4.k.a	$61$	$4$	61.k	61.k	$30$	$112$	$14$	$3.599$		None		$2$	$0$	\(-7\)	\(-18\)	\(47\)	\(-3\)			$\mathrm{SU}(2)[C_{30}]$
61.5.d.a	$61$	$5$	61.d	61.d	$4$	$38$	$19$	$6.306$		None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-22\)			$\mathrm{SU}(2)[C_{4}]$
61.5.h.a	$61$	$5$	61.h	61.h	$12$	$80$	$20$	$6.306$		None		$2$	$0$	\(-4\)	\(0\)	\(66\)	\(2\)			$\mathrm{SU}(2)[C_{12}]$
61.5.j.a	$61$	$5$	61.j	61.j	$20$	$152$	$19$	$6.306$		None		$2$	$0$	\(-8\)	\(-10\)	\(-130\)	\(12\)			$\mathrm{SU}(2)[C_{20}]$
61.5.l.a	$61$	$5$	61.l	61.l	$60$	$320$	$20$	$6.306$		None		$2$	$0$	\(-16\)	\(-20\)	\(34\)	\(-22\)			$\mathrm{SU}(2)[C_{60}]$
61.6.a.a	$61$	$6$	61.a	1.a	$1$	$11$	$11$	$9.783$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-9\)	\(-46\)	\(-129\)	\(-87\)	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-4+\beta _{7})q^{3}+(11+\cdots)q^{4}+\cdots\)
61.6.a.b	$61$	$6$	61.a	1.a	$1$	$14$	$14$	$9.783$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(11\)	\(26\)	\(71\)	\(109\)	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{5})q^{3}+(19-\beta _{1}+\cdots)q^{4}+\cdots\)
61.6.b.a	$61$	$6$	61.b	61.b	$2$	$26$	$26$	$9.783$		None		$2$	$0$	\(0\)	\(-20\)	\(-128\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
61.6.c.a	$61$	$6$	61.c	61.c	$3$	$48$	$24$	$9.783$		None		$2$	$0$	\(-5\)	\(-22\)	\(46\)	\(-113\)			$\mathrm{SU}(2)[C_{3}]$
61.6.e.a	$61$	$6$	61.e	61.e	$5$	$100$	$25$	$9.783$		None		$2$	$0$	\(-7\)	\(15\)	\(93\)	\(-262\)			$\mathrm{SU}(2)[C_{5}]$
61.6.f.a	$61$	$6$	61.f	61.f	$6$	$50$	$25$	$9.783$		None		$2$	$0$	\(-3\)	\(-22\)	\(11\)	\(207\)			$\mathrm{SU}(2)[C_{6}]$
61.6.g.a	$61$	$6$	61.g	61.g	$10$	$104$	$26$	$9.783$		None		$2$	$0$	\(-5\)	\(15\)	\(-122\)	\(230\)			$\mathrm{SU}(2)[C_{10}]$
61.6.i.a	$61$	$6$	61.i	61.i	$15$	$192$	$24$	$9.783$		None		$2$	$0$	\(-5\)	\(12\)	\(-96\)	\(-407\)			$\mathrm{SU}(2)[C_{15}]$
61.6.k.a	$61$	$6$	61.k	61.k	$30$	$200$	$25$	$9.783$		None		$2$	$0$	\(-7\)	\(12\)	\(224\)	\(293\)			$\mathrm{SU}(2)[C_{30}]$
61.7.d.a	$61$	$7$	61.d	61.d	$4$	$60$	$30$	$14.033$		None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(-258\)			$\mathrm{SU}(2)[C_{4}]$
61.7.h.a	$61$	$7$	61.h	61.h	$12$	$120$	$30$	$14.033$		None		$2$	$0$	\(-12\)	\(0\)	\(126\)	\(1644\)			$\mathrm{SU}(2)[C_{12}]$
61.7.j.a	$61$	$7$	61.j	61.j	$20$	$240$	$30$	$14.033$		None		$2$	$0$	\(-16\)	\(-10\)	\(-230\)	\(248\)			$\mathrm{SU}(2)[C_{20}]$
61.7.l.a	$61$	$7$	61.l	61.l	$60$	$480$	$30$	$14.033$		None		$2$	$0$	\(-8\)	\(-20\)	\(74\)	\(-1664\)			$\mathrm{SU}(2)[C_{60}]$
61.8.a.a	$61$	$8$	61.a	1.a	$1$	$16$	$16$	$19.055$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-17\)	\(-82\)	\(-571\)	\(-355\)	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-5-\beta _{5})q^{3}+(46+\cdots)q^{4}+\cdots\)
61.8.a.b	$61$	$8$	61.a	1.a	$1$	$19$	$19$	$19.055$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(23\)	\(134\)	\(429\)	\(1017\)	$+$	$2^{13}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(7+\beta _{3})q^{3}+(69+2\beta _{1}+\cdots)q^{4}+\cdots\)
61.8.b.a	$61$	$8$	61.b	61.b	$2$	$34$	$34$	$19.055$		None		$2$	$0$	\(0\)	\(52\)	\(696\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
61.8.c.a	$61$	$8$	61.c	61.c	$3$	$72$	$36$	$19.055$		None		$2$	$0$	\(-9\)	\(50\)	\(-446\)	\(-1681\)			$\mathrm{SU}(2)[C_{3}]$
61.8.e.a	$61$	$8$	61.e	61.e	$5$	$140$	$35$	$19.055$		None		$2$	$0$	\(-11\)	\(-57\)	\(-833\)	\(1978\)			$\mathrm{SU}(2)[C_{5}]$
61.8.f.a	$61$	$8$	61.f	61.f	$6$	$70$	$35$	$19.055$		None		$2$	$0$	\(-3\)	\(50\)	\(-27\)	\(495\)			$\mathrm{SU}(2)[C_{6}]$
61.8.g.a	$61$	$8$	61.g	61.g	$10$	$136$	$34$	$19.055$		None		$2$	$0$	\(-5\)	\(-57\)	\(414\)	\(-2650\)			$\mathrm{SU}(2)[C_{10}]$
61.8.i.a	$61$	$8$	61.i	61.i	$15$	$288$	$36$	$19.055$		None		$2$	$0$	\(-1\)	\(-60\)	\(1406\)	\(-4759\)			$\mathrm{SU}(2)[C_{15}]$
61.8.k.a	$61$	$8$	61.k	61.k	$30$	$280$	$35$	$19.055$		None		$2$	$0$	\(-7\)	\(-60\)	\(-1098\)	\(5925\)			$\mathrm{SU}(2)[C_{30}]$
61.9.d.a	$61$	$9$	61.d	61.d	$4$	$82$	$41$	$24.850$		None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-7502\)			$\mathrm{SU}(2)[C_{4}]$