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 266 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.2.a.a	$15$	$2$	15.a	1.a	$1$	$1$	$1$	$0.120$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
15.3.c.a	$15$	$3$	15.c	3.b	$2$	$2$	$2$	$0.409$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-12\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)
15.3.d.a	$15$	$3$	15.d	15.d	$2$	$1$	$1$	$0.409$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-1\)	\(3\)	\(-5\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots\)
15.3.d.b	$15$	$3$	15.d	15.d	$2$	$1$	$1$	$0.409$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(1\)	\(-3\)	\(5\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)
15.3.f.a	$15$	$3$	15.f	5.c	$4$	$4$	$2$	$0.409$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
15.4.a.a	$15$	$4$	15.a	1.a	$1$	$1$	$1$	$0.885$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(3\)	\(5\)	\(-24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
15.4.a.b	$15$	$4$	15.a	1.a	$1$	$1$	$1$	$0.885$	\(\Q\)	None	✓	$1$	$0$	\(3\)	\(-3\)	\(-5\)	\(20\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots\)
15.4.b.a	$15$	$4$	15.b	5.b	$2$	$4$	$4$	$0.885$	\(\Q(i, \sqrt{41})\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
15.4.e.a	$15$	$4$	15.e	15.e	$4$	$8$	$4$	$0.885$	8.0.\(\cdots\).8	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(-16\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
15.5.c.a	$15$	$5$	15.c	3.b	$2$	$6$	$6$	$1.551$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(76\)		$3\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
15.5.d.a	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-7\)	\(9\)	\(25\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.b	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(7\)	\(-9\)	\(-25\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.c	$15$	$5$	15.d	15.d	$2$	$4$	$4$	$1.551$	\(\Q(\sqrt{10}, \sqrt{-26})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
15.5.f.a	$15$	$5$	15.f	5.c	$4$	$8$	$4$	$1.551$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-84\)	\(20\)		$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
15.6.a.a	$15$	$6$	15.a	1.a	$1$	$1$	$1$	$2.406$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-9\)	\(-25\)	\(-132\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-9q^{3}-28q^{4}-5^{2}q^{5}+18q^{6}+\cdots\)
15.6.a.b	$15$	$6$	15.a	1.a	$1$	$1$	$1$	$2.406$	\(\Q\)	None	✓	$1$	$0$	\(7\)	\(9\)	\(-25\)	\(12\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+7q^{2}+9q^{3}+17q^{4}-5^{2}q^{5}+63q^{6}+\cdots\)
15.6.a.c	$15$	$6$	15.a	1.a	$1$	$2$	$2$	$2.406$	\(\Q(\sqrt{409}) \)	None	✓	$1$	$0$	\(-1\)	\(-18\)	\(50\)	\(-112\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-9q^{3}+(70+\beta )q^{4}+5^{2}q^{5}+\cdots\)
15.6.b.a	$15$	$6$	15.b	5.b	$2$	$4$	$4$	$2.406$	\(\Q(i, \sqrt{89})\)	None		$2$	$0$	\(0\)	\(0\)	\(120\)	\(0\)		$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-11+\beta _{3})q^{4}+\cdots\)
15.6.e.a	$15$	$6$	15.e	15.e	$4$	$16$	$8$	$2.406$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-80\)		$2^{9}\cdot 3^{10}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-13\beta _{3}-\beta _{6})q^{4}+\cdots\)
15.7.c.a	$15$	$7$	15.c	3.b	$2$	$8$	$8$	$3.451$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(20\)	\(0\)	\(160\)		$2\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(2-\beta _{5})q^{3}+(-41-\beta _{3}+\cdots)q^{4}+\cdots\)
15.7.d.a	$15$	$7$	15.d	15.d	$2$	$1$	$1$	$3.451$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-11\)	\(-27\)	\(125\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-11q^{2}-3^{3}q^{3}+57q^{4}+5^{3}q^{5}+\cdots\)
15.7.d.b	$15$	$7$	15.d	15.d	$2$	$1$	$1$	$3.451$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(11\)	\(27\)	\(-125\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+11q^{2}+3^{3}q^{3}+57q^{4}-5^{3}q^{5}+\cdots\)
15.7.d.c	$15$	$7$	15.d	15.d	$2$	$8$	$8$	$3.451$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{7}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots\)
15.7.f.a	$15$	$7$	15.f	5.c	$4$	$12$	$6$	$3.451$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(16\)	\(0\)	\(136\)	\(-696\)		$2\cdot 3^{10}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1}-\beta _{4})q^{2}-\beta _{6}q^{3}+(18\beta _{1}+\cdots)q^{4}+\cdots\)
15.8.a.a	$15$	$8$	15.a	1.a	$1$	$1$	$1$	$4.686$	\(\Q\)	None	✓	$1$	$1$	\(-22\)	\(27\)	\(-125\)	\(-420\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-22q^{2}+3^{3}q^{3}+356q^{4}-5^{3}q^{5}+\cdots\)
15.8.a.b	$15$	$8$	15.a	1.a	$1$	$1$	$1$	$4.686$	\(\Q\)	None	✓	$1$	$0$	\(-13\)	\(-27\)	\(-125\)	\(1380\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-13q^{2}-3^{3}q^{3}+41q^{4}-5^{3}q^{5}+\cdots\)
15.8.a.c	$15$	$8$	15.a	1.a	$1$	$2$	$2$	$4.686$	\(\Q(\sqrt{601}) \)	None	✓	$1$	$0$	\(7\)	\(54\)	\(250\)	\(1304\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(4-\beta )q^{2}+3^{3}q^{3}+(38-7\beta )q^{4}+\cdots\)
15.8.b.a	$15$	$8$	15.b	5.b	$2$	$8$	$8$	$4.686$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-444\)	\(0\)		$2^{4}\cdot 3^{12}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-83-\beta _{4})q^{4}+\cdots\)
15.8.e.a	$15$	$8$	15.e	15.e	$4$	$24$	$12$	$4.686$		None		$4$	$0$	\(0\)	\(24\)	\(0\)	\(1344\)			$\mathrm{SU}(2)[C_{4}]$
15.9.c.a	$15$	$9$	15.c	3.b	$2$	$10$	$10$	$6.111$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(-112\)	\(0\)	\(7156\)		$2^{4}\cdot 3^{10}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-11-2\beta _{1}-\beta _{2})q^{3}+(-79+\cdots)q^{4}+\cdots\)
15.9.d.a	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-17\)	\(-81\)	\(-625\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots\)
15.9.d.b	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(17\)	\(81\)	\(625\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots\)
15.9.d.c	$15$	$9$	15.d	15.d	$2$	$12$	$12$	$6.111$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{13}\cdot 3^{18}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots\)
15.9.f.a	$15$	$9$	15.f	5.c	$4$	$16$	$8$	$6.111$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-444\)	\(4540\)		$2^{11}\cdot 3^{20}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}-\beta _{6}q^{3}+(158\beta _{1}-3\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)
15.10.a.a	$15$	$10$	15.a	1.a	$1$	$1$	$1$	$7.726$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(81\)	\(625\)	\(-7680\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots\)
15.10.a.b	$15$	$10$	15.a	1.a	$1$	$1$	$1$	$7.726$	\(\Q\)	None	✓	$1$	$1$	\(22\)	\(-81\)	\(-625\)	\(-5988\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots\)
15.10.a.c	$15$	$10$	15.a	1.a	$1$	$2$	$2$	$7.726$	\(\Q(\sqrt{4729}) \)	None	✓	$1$	$0$	\(19\)	\(162\)	\(-1250\)	\(-11872\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots\)
15.10.a.d	$15$	$10$	15.a	1.a	$1$	$2$	$2$	$7.726$	\(\Q(\sqrt{241}) \)	None	✓	$1$	$0$	\(31\)	\(-162\)	\(1250\)	\(14112\)	$-$	$3$	$\mathrm{SU}(2)$	\(q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots\)
15.10.b.a	$15$	$10$	15.b	5.b	$2$	$8$	$8$	$7.726$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-690\)	\(0\)		$2^{3}\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{4}q^{3}+(-149-\beta _{1})q^{4}+\cdots\)
15.10.e.a	$15$	$10$	15.e	15.e	$4$	$32$	$16$	$7.726$		None		$4$	$0$	\(0\)	\(-150\)	\(0\)	\(-9760\)			$\mathrm{SU}(2)[C_{4}]$
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		$2$	$0$	\(-64\)	\(0\)	\(10676\)	\(10604\)		$2^{21}\cdot 3^{34}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-3-3\beta _{2}-\beta _{3})q^{2}+\beta _{6}q^{3}+(451\beta _{2}+\cdots)q^{4}+\cdots\)
15.12.a.a	$15$	$12$	15.a	1.a	$1$	$1$	$1$	$11.525$	\(\Q\)	None	✓	$1$	$1$	\(-56\)	\(-243\)	\(3125\)	\(27984\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots\)
15.12.a.b	$15$	$12$	15.a	1.a	$1$	$2$	$2$	$11.525$	\(\Q(\sqrt{1609}) \)	None	✓	$1$	$1$	\(-22\)	\(486\)	\(-6250\)	\(-10864\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots\)
15.12.a.c	$15$	$12$	15.a	1.a	$1$	$2$	$2$	$11.525$	\(\Q(\sqrt{1801}) \)	None	✓	$1$	$0$	\(-13\)	\(-486\)	\(-6250\)	\(7784\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots\)
15.12.a.d	$15$	$12$	15.a	1.a	$1$	$3$	$3$	$11.525$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(729\)	\(9375\)	\(-14608\)	$+$	$2\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots\)
15.12.b.a	$15$	$12$	15.b	5.b	$2$	$12$	$12$	$11.525$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2556\)	\(0\)		$2^{10}\cdot 3^{28}\cdot 5^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots\)