Newform search results

Results (32 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.2.a.a	$23$	$2$	23.a	1.a	$1$	$2$	$2$	$0.184$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
23.2.c.a	$23$	$2$	23.c	23.c	$11$	$10$	$1$	$0.184$	\(\Q(\zeta_{22})\)	None		$2$	$0$	\(-7\)	\(-7\)	\(-3\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
23.3.b.a	$23$	$3$	23.b	23.b	$2$	$3$	$3$	$0.627$	3.3.621.1	\(\Q(\sqrt{-23}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
23.3.d.a	$23$	$3$	23.d	23.d	$22$	$30$	$3$	$0.627$		None		$2$	$0$	\(-11\)	\(-11\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
23.4.a.a	$23$	$4$	23.a	1.a	$1$	$1$	$1$	$1.357$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-5\)	\(-6\)	\(-8\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots\)
23.4.a.b	$23$	$4$	23.a	1.a	$1$	$4$	$4$	$1.357$	4.4.334189.1	None	✓	$1$	$0$	\(2\)	\(7\)	\(14\)	\(16\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots\)
23.4.c.a	$23$	$4$	23.c	23.c	$11$	$50$	$5$	$1.357$		None		$2$	$0$	\(-11\)	\(-13\)	\(-19\)	\(-19\)			$\mathrm{SU}(2)[C_{11}]$
23.5.b.a	$23$	$5$	23.b	23.b	$2$	$3$	$3$	$2.378$	3.3.621.1	\(\Q(\sqrt{-23}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}-2\beta _{2})q^{2}+(6\beta _{1}-\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\)
23.5.b.b	$23$	$5$	23.b	23.b	$2$	$4$	$4$	$2.378$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(-8\)	\(-12\)	\(0\)	\(0\)		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2-\beta _{3})q^{2}+(-3+3\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots\)
23.5.d.a	$23$	$5$	23.d	23.d	$22$	$70$	$7$	$2.378$		None		$2$	$0$	\(-3\)	\(1\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
23.6.a.a	$23$	$6$	23.a	1.a	$1$	$3$	$3$	$3.689$	3.3.7925.1	None	✓	$1$	$1$	\(-4\)	\(-20\)	\(-58\)	\(-282\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-7-2\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.6.a.b	$23$	$6$	23.a	1.a	$1$	$6$	$6$	$3.689$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(16\)	\(42\)	\(300\)	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{4})q^{3}+(19+\cdots)q^{4}+\cdots\)
23.6.c.a	$23$	$6$	23.c	23.c	$11$	$90$	$9$	$3.689$		None		$2$	$0$	\(-11\)	\(-7\)	\(5\)	\(-29\)			$\mathrm{SU}(2)[C_{11}]$
23.7.b.a	$23$	$7$	23.b	23.b	$2$	$1$	$1$	$5.291$	\(\Q\)	\(\Q(\sqrt{-23}) \)	✓	$2$	$0$	\(-7\)	\(-38\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-7q^{2}-38q^{3}-15q^{4}+266q^{6}+\cdots\)
23.7.b.b	$23$	$7$	23.b	23.b	$2$	$2$	$2$	$5.291$	\(\Q(\sqrt{69}) \)	\(\Q(\sqrt{-23}) \)	✓	$2$	$0$	\(7\)	\(38\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2+3\beta )q^{2}+(23-8\beta )q^{3}+(93+21\beta )q^{4}+\cdots\)
23.7.b.c	$23$	$7$	23.b	23.b	$2$	$8$	$8$	$5.291$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(8\)	\(30\)	\(0\)	\(0\)		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{2}+(4+\beta _{3})q^{3}+(21-3\beta _{1}+\cdots)q^{4}+\cdots\)
23.7.d.a	$23$	$7$	23.d	23.d	$22$	$110$	$11$	$5.291$		None		$2$	$0$	\(-19\)	\(-41\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
23.8.a.a	$23$	$8$	23.a	1.a	$1$	$5$	$5$	$7.185$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(-16\)	\(-68\)	\(-56\)	\(-1156\)	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{2}+(-14+\beta _{2})q^{3}+(51+\cdots)q^{4}+\cdots\)
23.8.a.b	$23$	$8$	23.a	1.a	$1$	$8$	$8$	$7.185$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(40\)	\(444\)	\(1446\)	$+$	$2^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(5-\beta _{1}+\beta _{2})q^{3}+(80+2\beta _{1}+\cdots)q^{4}+\cdots\)
23.8.c.a	$23$	$8$	23.c	23.c	$11$	$130$	$13$	$7.185$		None		$2$	$0$	\(5\)	\(17\)	\(-399\)	\(-301\)			$\mathrm{SU}(2)[C_{11}]$
23.9.b.a	$23$	$9$	23.b	23.b	$2$	$3$	$3$	$9.370$	3.3.621.1	\(\Q(\sqrt{-23}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$7$	$\mathrm{U}(1)[D_{2}]$	\(q+(-3\beta _{1}-2\beta _{2})q^{2}+(13\beta _{1}-17\beta _{2})q^{3}+\cdots\)
23.9.b.b	$23$	$9$	23.b	23.b	$2$	$12$	$12$	$9.370$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-8\)	\(-72\)	\(0\)	\(0\)		$2^{13}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+(-6+\beta _{3})q^{3}+(30+\cdots)q^{4}+\cdots\)
23.9.d.a	$23$	$9$	23.d	23.d	$22$	$150$	$15$	$9.370$		None		$2$	$0$	\(-3\)	\(61\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
23.10.a.a	$23$	$10$	23.a	1.a	$1$	$7$	$7$	$11.846$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-89\)	\(-2388\)	\(-9896\)	$+$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-13-2\beta _{1}-\beta _{4})q^{3}+(220+\cdots)q^{4}+\cdots\)
23.10.a.b	$23$	$10$	23.a	1.a	$1$	$10$	$10$	$11.846$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(32\)	\(235\)	\(112\)	\(1280\)	$-$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{2}+(23+\beta _{1}+\beta _{3})q^{3}+(307+\cdots)q^{4}+\cdots\)
23.10.c.a	$23$	$10$	23.c	23.c	$11$	$170$	$17$	$11.846$		None		$2$	$0$	\(-43\)	\(-157\)	\(2265\)	\(8605\)			$\mathrm{SU}(2)[C_{11}]$
23.11.b.a	$23$	$11$	23.b	23.b	$2$	$3$	$3$	$14.613$	3.3.621.1	\(\Q(\sqrt{-23}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-23\beta _{1}-2\beta _{2})q^{2}+(-66\beta _{1}+119\beta _{2})q^{3}+\cdots\)
23.11.b.b	$23$	$11$	23.b	23.b	$2$	$16$	$16$	$14.613$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-24\)	\(60\)	\(0\)	\(0\)		$2^{23}\cdot 3^{11}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta _{2})q^{2}+(4-\beta _{2}-\beta _{3})q^{3}+\cdots\)
23.11.d.a	$23$	$11$	23.d	23.d	$22$	$190$	$19$	$14.613$		None		$2$	$0$	\(13\)	\(-71\)	\(-11\)	\(-11\)			$\mathrm{SU}(2)[C_{22}]$
23.12.a.a	$23$	$12$	23.a	1.a	$1$	$8$	$8$	$17.672$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-32\)	\(-992\)	\(-11466\)	\(-54118\)	$-$	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-4-\beta _{1})q^{2}+(-124-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
23.12.a.b	$23$	$12$	23.a	1.a	$1$	$11$	$11$	$17.672$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(32\)	\(-20\)	\(1034\)	\(159584\)	$+$	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.12.c.a	$23$	$12$	23.c	23.c	$11$	$210$	$21$	$17.672$		None		$2$	$0$	\(37\)	\(497\)	\(761\)	\(-71989\)			$\mathrm{SU}(2)[C_{11}]$