Newform search results

Results (1-50 of )

  To download results, .

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.11.b.a	$3$	$11$	3.b	3.b	$2$	$2$	$2$	$1.906$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(-54\)	\(0\)	\(34468\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-3^{3}+9\beta )q^{3}+304q^{4}+\cdots\)
4.11.b.a	$4$	$11$	4.b	4.b	$2$	$4$	$4$	$2.541$	4.0.26777625.2	None		$2$	$0$	\(-12\)	\(0\)	\(-1560\)	\(0\)	$2^{12}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3+\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
5.11.c.a	$5$	$11$	5.c	5.c	$4$	$8$	$4$	$3.177$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(30\)	\(60\)	\(-5340\)	\(-14500\)	$2^{8}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(4+4\beta _{1}-\beta _{3})q^{2}+(8-8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
6.11.b.a	$6$	$11$	6.b	3.b	$2$	$4$	$4$	$3.812$	\(\Q(\sqrt{-2}, \sqrt{85})\)	None		$2$	$0$	\(0\)	\(84\)	\(0\)	\(-45112\)	$2^{11}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(21-3\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
7.11.b.a	$7$	$11$	7.b	7.b	$2$	$1$	$1$	$4.448$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(57\)	\(0\)	\(0\)	\(-16807\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+57q^{2}+2225q^{4}-7^{5}q^{7}+68457q^{8}+\cdots\)
7.11.b.b	$7$	$11$	7.b	7.b	$2$	$4$	$4$	$4.448$	4.0.373770240.2	None		$2$	$0$	\(-48\)	\(0\)	\(0\)	\(4900\)	$2^{7}\cdot 3\cdot 5\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-12+\beta _{2})q^{2}-\beta _{1}q^{3}+(-12^{2}+\cdots)q^{4}+\cdots\)
7.11.d.a	$7$	$11$	7.d	7.d	$6$	$12$	$6$	$4.448$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-12\)	\(-246\)	\(3330\)	\(-12572\)	$2^{10}\cdot 3^{4}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-\beta _{1}-2\beta _{2})q^{2}+(-3^{3}+2\beta _{1}+\cdots)q^{3}+\cdots\)
8.11.d.a	$8$	$11$	8.d	8.d	$2$	$1$	$1$	$5.083$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-32\)	\(-482\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots\)
8.11.d.b	$8$	$11$	8.d	8.d	$2$	$8$	$8$	$5.083$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(42\)	\(480\)	\(0\)	\(0\)	$2^{28}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(5-\beta _{1})q^{2}+(60+\beta _{1}+\beta _{2})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)
9.11.b.a	$9$	$11$	9.b	3.b	$2$	$4$	$4$	$5.718$	\(\Q(\sqrt{-2}, \sqrt{385})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-44464\)	$2\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots\)
9.11.d.a	$9$	$11$	9.d	9.d	$6$	$18$	$9$	$5.718$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-3\)	\(51\)	\(4956\)	\(-6120\)	$2^{14}\cdot 3^{36}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
10.11.c.a	$10$	$11$	10.c	5.c	$4$	$2$	$1$	$6.354$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(32\)	\(-366\)	\(-3750\)	\(-16814\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{4}+2^{4}i)q^{2}+(-183+183i)q^{3}+\cdots\)
10.11.c.b	$10$	$11$	10.c	5.c	$4$	$2$	$1$	$6.354$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(32\)	\(114\)	\(5850\)	\(13906\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{4}+2^{4}i)q^{2}+(57-57i)q^{3}+2^{9}iq^{4}+\cdots\)
10.11.c.c	$10$	$11$	10.c	5.c	$4$	$6$	$3$	$6.354$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(-96\)	\(128\)	\(5460\)	\(13512\)	$2^{8}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{4}-2^{4}\beta _{1})q^{2}+(21-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
11.11.b.a	$11$	$11$	11.b	11.b	$2$	$1$	$1$	$6.989$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(475\)	\(-3001\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+475q^{3}+2^{10}q^{4}-3001q^{5}+166576q^{9}+\cdots\)
11.11.b.b	$11$	$11$	11.b	11.b	$2$	$8$	$8$	$6.989$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-402\)	\(2430\)	\(0\)	$2^{8}\cdot 3^{3}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-50+\beta _{2})q^{3}+(-22^{2}+\cdots)q^{4}+\cdots\)
11.11.d.a	$11$	$11$	11.d	11.d	$10$	$36$	$9$	$6.989$		None		$2$	$0$	\(-5\)	\(-78\)	\(566\)	\(-9740\)		$\mathrm{SU}(2)[C_{10}]$
12.11.c.a	$12$	$11$	12.c	3.b	$2$	$1$	$1$	$7.624$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-243\)	\(0\)	\(22082\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{5}q^{3}+22082q^{7}+3^{10}q^{9}+702218q^{13}+\cdots\)
12.11.c.b	$12$	$11$	12.c	3.b	$2$	$2$	$2$	$7.624$	\(\Q(\sqrt{-35}) \)	None		$2$	$0$	\(0\)	\(234\)	\(0\)	\(-20636\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(117+\beta )q^{3}+6\beta q^{5}-10318q^{7}+\cdots\)
12.11.d.a	$12$	$11$	12.d	4.b	$2$	$10$	$10$	$7.624$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(22\)	\(0\)	\(3116\)	\(0\)	$2^{39}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\beta _{2})q^{2}+\beta _{1}q^{3}+(-65-2\beta _{1}+\cdots)q^{4}+\cdots\)
13.11.d.a	$13$	$11$	13.d	13.d	$4$	$20$	$10$	$8.260$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-34\)	\(-4\)	\(-7792\)	\(-38312\)	$2^{20}\cdot 3^{6}\cdot 13^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2-2\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
13.11.f.a	$13$	$11$	13.f	13.f	$12$	$44$	$11$	$8.260$		None		$2$	$0$	\(28\)	\(-2\)	\(7786\)	\(30856\)		$\mathrm{SU}(2)[C_{12}]$
14.11.b.a	$14$	$11$	14.b	7.b	$2$	$8$	$8$	$8.895$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(18376\)	$2^{28}\cdot 3^{2}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+2^{9}q^{4}+(-3\beta _{3}+\cdots)q^{5}+\cdots\)
14.11.d.a	$14$	$11$	14.d	7.d	$6$	$12$	$6$	$8.895$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(486\)	\(-6666\)	\(30576\)	$2^{24}\cdot 3^{4}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(54+3^{3}\beta _{1}-2\beta _{2}-2\beta _{3}+\cdots)q^{3}+\cdots\)
15.11.c.a	$15$	$11$	15.c	3.b	$2$	$14$	$14$	$9.530$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(44\)	\(0\)	\(-50548\)	$2^{9}\cdot 3^{20}\cdot 5^{21}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(3+\beta _{2}-\beta _{3})q^{3}+(-629+\cdots)q^{4}+\cdots\)
15.11.d.a	$15$	$11$	15.d	15.d	$2$	$1$	$1$	$9.530$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-61\)	\(243\)	\(-3125\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-61q^{2}+3^{5}q^{3}+2697q^{4}-5^{5}q^{5}+\cdots\)
15.11.d.b	$15$	$11$	15.d	15.d	$2$	$1$	$1$	$9.530$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(61\)	\(-243\)	\(3125\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+61q^{2}-3^{5}q^{3}+2697q^{4}+5^{5}q^{5}+\cdots\)
15.11.d.c	$15$	$11$	15.d	15.d	$2$	$16$	$16$	$9.530$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{32}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(137-\beta _{2}+\cdots)q^{4}+\cdots\)
15.11.f.a	$15$	$11$	15.f	5.c	$4$	$20$	$10$	$9.530$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-64\)	\(0\)	\(10676\)	\(10604\)	$2^{21}\cdot 3^{34}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-3-3\beta _{2}-\beta _{3})q^{2}+\beta _{6}q^{3}+(451\beta _{2}+\cdots)q^{4}+\cdots\)
16.11.c.a	$16$	$11$	16.c	4.b	$2$	$1$	$1$	$10.166$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(474\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+474q^{5}+3^{10}q^{9}+683050q^{13}+\cdots\)
16.11.c.b	$16$	$11$	16.c	4.b	$2$	$4$	$4$	$10.166$	\(\Q(\sqrt{-3}, \sqrt{505})\)	None		$2$	$0$	\(0\)	\(0\)	\(4200\)	\(0\)	$2^{25}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(1050+\beta _{2})q^{5}+(-12\beta _{1}+\cdots)q^{7}+\cdots\)
16.11.f.a	$16$	$11$	16.f	16.f	$4$	$38$	$19$	$10.166$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$
17.11.e.a	$17$	$11$	17.e	17.e	$16$	$112$	$14$	$10.801$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$
18.11.b.a	$18$	$11$	18.b	3.b	$2$	$2$	$2$	$11.436$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(41272\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}\beta q^{2}-2^{9}q^{4}-1443\beta q^{5}+20636q^{7}+\cdots\)
18.11.d.a	$18$	$11$	18.d	9.d	$6$	$20$	$10$	$11.436$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(-84\)	\(-9918\)	\(12238\)	$2^{46}\cdot 3^{37}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-2-4\beta _{1}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
19.11.b.a	$19$	$11$	19.b	19.b	$2$	$1$	$1$	$12.072$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(3951\)	\(-32525\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{10}q^{4}+3951q^{5}-32525q^{7}+\cdots\)
19.11.b.b	$19$	$11$	19.b	19.b	$2$	$14$	$14$	$12.072$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2842\)	\(-3840\)	$2^{13}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-599+\beta _{2})q^{4}+\cdots\)
19.11.d.a	$19$	$11$	19.d	19.d	$6$	$30$	$15$	$12.072$		None		$2$	$0$	\(-3\)	\(63\)	\(-1112\)	\(42200\)		$\mathrm{SU}(2)[C_{6}]$
19.11.f.a	$19$	$11$	19.f	19.f	$18$	$96$	$16$	$12.072$		None		$2$	$0$	\(-6\)	\(-72\)	\(-6\)	\(-5844\)		$\mathrm{SU}(2)[C_{18}]$
20.11.b.a	$20$	$11$	20.b	4.b	$2$	$20$	$20$	$12.707$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(22\)	\(0\)	\(0\)	\(0\)	$2^{94}\cdot 3^{4}\cdot 5^{29}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-2^{5}+\cdots)q^{4}+\cdots\)
20.11.d.a	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(-32\)	\(-236\)	\(-3125\)	\(-33364\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}-236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
20.11.d.b	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(32\)	\(236\)	\(-3125\)	\(33364\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{5}q^{2}+236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
20.11.d.c	$20$	$11$	20.d	20.d	$2$	$2$	$2$	$12.707$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-474\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+8iq^{2}-2^{10}q^{4}+(-237+779i)q^{5}+\cdots\)
20.11.d.d	$20$	$11$	20.d	20.d	$2$	$24$	$24$	$12.707$		None		$4$	$0$	\(0\)	\(0\)	\(8280\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
20.11.f.a	$20$	$11$	20.f	5.c	$4$	$10$	$5$	$12.707$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(62\)	\(894\)	\(22286\)	$2^{22}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(6+6\beta _{1}-\beta _{2})q^{3}+(90-174\beta _{1}+\cdots)q^{5}+\cdots\)
21.11.b.a	$21$	$11$	21.b	3.b	$2$	$20$	$20$	$13.343$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(106\)	\(0\)	\(0\)	$2^{17}\cdot 3^{34}\cdot 7^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(5+\beta _{4})q^{3}+(-573+\beta _{3}+\cdots)q^{4}+\cdots\)
21.11.d.a	$21$	$11$	21.d	7.b	$2$	$14$	$14$	$13.343$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-22\)	\(0\)	\(0\)	\(7734\)	$2^{15}\cdot 3^{25}\cdot 7^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta _{1})q^{2}-\beta _{4}q^{3}+(498-6\beta _{1}+\cdots)q^{4}+\cdots\)
21.11.f.a	$21$	$11$	21.f	7.d	$6$	$12$	$6$	$13.343$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(11\)	\(-1458\)	\(-1287\)	\(20090\)	$2^{10}\cdot 3^{7}\cdot 7^{7}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+2\beta _{2})q^{2}+(-3^{4}-3^{4}\beta _{2}+\cdots)q^{3}+\cdots\)
21.11.f.b	$21$	$11$	21.f	7.d	$6$	$14$	$7$	$13.343$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(11\)	\(1701\)	\(-5379\)	\(-21705\)	$2^{8}\cdot 3^{9}\cdot 7^{7}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-2\beta _{3})q^{2}+(3^{4}-3^{4}\beta _{3})q^{3}+\cdots\)
21.11.h.a	$21$	$11$	21.h	21.h	$6$	$2$	$1$	$13.343$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(243\)	\(0\)	\(10907\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+3^{5}\zeta_{6}q^{3}-2^{10}\zeta_{6}q^{4}+(-3725+\cdots)q^{7}+\cdots\)

  To download results, .