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 80 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
29.2.a.a	$29$	$2$	29.a	1.a	$1$	$2$	$2$	$0.232$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
29.2.b.a	$29$	$2$	29.b	29.b	$2$	$2$	$2$	$0.232$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)
29.2.d.a	$29$	$2$	29.d	29.d	$7$	$6$	$1$	$0.232$	\(\Q(\zeta_{14})\)	None		$2$	$0$	\(-2\)	\(-5\)	\(1\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
29.2.e.a	$29$	$2$	29.e	29.e	$14$	$12$	$2$	$0.232$	12.0.\(\cdots\).1	None		$2$	$0$	\(-7\)	\(-7\)	\(-1\)	\(-11\)		$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)
29.3.c.a	$29$	$3$	29.c	29.c	$4$	$8$	$4$	$0.790$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(2\)	\(-2\)	\(0\)	\(-4\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
29.3.f.a	$29$	$3$	29.f	29.f	$28$	$48$	$4$	$0.790$		None		$2$	$0$	\(-16\)	\(-12\)	\(-14\)	\(-10\)			$\mathrm{SU}(2)[C_{28}]$
29.4.a.a	$29$	$4$	29.a	1.a	$1$	$2$	$2$	$1.711$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(-10\)	\(-10\)	\(-16\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
29.4.a.b	$29$	$4$	29.a	1.a	$1$	$5$	$5$	$1.711$	5.5.13458092.1	None	✓	$1$	$0$	\(0\)	\(8\)	\(10\)	\(40\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots\)
29.4.b.a	$29$	$4$	29.b	29.b	$2$	$6$	$6$	$1.711$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(22\)	\(-28\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-5+\beta _{4}+\beta _{5})q^{4}+\cdots\)
29.4.d.a	$29$	$4$	29.d	29.d	$7$	$42$	$7$	$1.711$		None		$2$	$0$	\(-5\)	\(-5\)	\(-7\)	\(-31\)			$\mathrm{SU}(2)[C_{7}]$
29.4.e.a	$29$	$4$	29.e	29.e	$14$	$36$	$6$	$1.711$		None		$2$	$0$	\(-7\)	\(-7\)	\(-29\)	\(21\)			$\mathrm{SU}(2)[C_{14}]$
29.5.c.a	$29$	$5$	29.c	29.c	$4$	$18$	$9$	$2.998$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-8\)	\(-2\)	\(0\)	\(-4\)		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{2}+6\beta _{4}+\cdots)q^{4}+\cdots\)
29.5.f.a	$29$	$5$	29.f	29.f	$28$	$108$	$9$	$2.998$		None		$2$	$0$	\(-6\)	\(-12\)	\(-14\)	\(-10\)			$\mathrm{SU}(2)[C_{28}]$
29.6.a.a	$29$	$6$	29.a	1.a	$1$	$4$	$4$	$4.651$	4.4.3257317.1	None	✓	$1$	$1$	\(0\)	\(-28\)	\(-68\)	\(-208\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.a.b	$29$	$6$	29.a	1.a	$1$	$7$	$7$	$4.651$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(26\)	\(32\)	\(184\)	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.b.a	$29$	$6$	29.b	29.b	$2$	$12$	$12$	$4.651$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(46\)	\(20\)		$2^{14}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-14+\beta _{2})q^{4}+\cdots\)
29.6.d.a	$29$	$6$	29.d	29.d	$7$	$66$	$11$	$4.651$		None		$2$	$0$	\(-11\)	\(-5\)	\(29\)	\(17\)			$\mathrm{SU}(2)[C_{7}]$
29.6.e.a	$29$	$6$	29.e	29.e	$14$	$72$	$12$	$4.651$		None		$2$	$0$	\(-7\)	\(-7\)	\(-53\)	\(-27\)			$\mathrm{SU}(2)[C_{14}]$
29.7.c.a	$29$	$7$	29.c	29.c	$4$	$28$	$14$	$6.672$		None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
29.7.f.a	$29$	$7$	29.f	29.f	$28$	$168$	$14$	$6.672$		None		$2$	$0$	\(-14\)	\(-12\)	\(-14\)	\(-10\)			$\mathrm{SU}(2)[C_{28}]$
29.8.a.a	$29$	$8$	29.a	1.a	$1$	$7$	$7$	$9.059$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-8\)	\(-82\)	\(-320\)	\(-1704\)	$-$	$2^{4}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-12+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
29.8.a.b	$29$	$8$	29.a	1.a	$1$	$10$	$10$	$9.059$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(80\)	\(180\)	\(1040\)	$+$	$2^{11}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(8+\beta _{2})q^{3}+(92+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
29.8.b.a	$29$	$8$	29.b	29.b	$2$	$16$	$16$	$9.059$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-198\)	\(660\)		$2^{17}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(-45+\beta _{2}+\cdots)q^{4}+\cdots\)
29.8.d.a	$29$	$8$	29.d	29.d	$7$	$102$	$17$	$9.059$		None		$2$	$0$	\(1\)	\(-5\)	\(133\)	\(657\)			$\mathrm{SU}(2)[C_{7}]$
29.8.e.a	$29$	$8$	29.e	29.e	$14$	$96$	$16$	$9.059$		None		$2$	$0$	\(-7\)	\(-7\)	\(191\)	\(-667\)			$\mathrm{SU}(2)[C_{14}]$
29.9.c.a	$29$	$9$	29.c	29.c	$4$	$38$	$19$	$11.814$		None		$2$	$0$	\(-8\)	\(-2\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
29.9.f.a	$29$	$9$	29.f	29.f	$28$	$228$	$19$	$11.814$		None		$2$	$0$	\(-6\)	\(-12\)	\(-14\)	\(-10\)			$\mathrm{SU}(2)[C_{28}]$
29.10.a.a	$29$	$10$	29.a	1.a	$1$	$9$	$9$	$14.936$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-244\)	\(-738\)	\(-7128\)	$+$	$2^{9}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-3^{3}-\beta _{4})q^{3}+(133+2\beta _{1}+\cdots)q^{4}+\cdots\)
29.10.a.b	$29$	$10$	29.a	1.a	$1$	$12$	$12$	$14.936$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(16\)	\(242\)	\(1762\)	\(12080\)	$-$	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(20+\beta _{1}-\beta _{3})q^{3}+(291+\cdots)q^{4}+\cdots\)
29.10.b.a	$29$	$10$	29.b	29.b	$2$	$22$	$22$	$14.936$		None		$2$	$0$	\(0\)	\(0\)	\(-1374\)	\(-4956\)			$\mathrm{SU}(2)[C_{2}]$
29.10.d.a	$29$	$10$	29.d	29.d	$7$	$126$	$21$	$14.936$		None		$2$	$0$	\(-23\)	\(-5\)	\(-1031\)	\(-4959\)			$\mathrm{SU}(2)[C_{7}]$
29.10.e.a	$29$	$10$	29.e	29.e	$14$	$132$	$22$	$14.936$		None		$2$	$0$	\(-7\)	\(-7\)	\(1367\)	\(4949\)			$\mathrm{SU}(2)[C_{14}]$
29.11.c.a	$29$	$11$	29.c	29.c	$4$	$48$	$24$	$18.425$		None		$2$	$0$	\(8\)	\(-2\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
29.11.f.a	$29$	$11$	29.f	29.f	$28$	$288$	$24$	$18.425$		None		$2$	$0$	\(-22\)	\(-12\)	\(-14\)	\(-10\)			$\mathrm{SU}(2)[C_{28}]$
29.12.a.a	$29$	$12$	29.a	1.a	$1$	$11$	$11$	$22.282$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-32\)	\(-982\)	\(-2740\)	\(-49432\)	$-$	$2^{13}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{2}+(-89-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
29.12.a.b	$29$	$12$	29.a	1.a	$1$	$14$	$14$	$22.282$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(476\)	\(9760\)	\(85024\)	$+$	$2^{20}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(34-\beta _{3})q^{3}+(1312+3\beta _{1}+\cdots)q^{4}+\cdots\)
29.12.b.a	$29$	$12$	29.b	29.b	$2$	$26$	$26$	$22.282$		None		$2$	$0$	\(0\)	\(0\)	\(3742\)	\(-2108\)			$\mathrm{SU}(2)[C_{2}]$
29.12.d.a	$29$	$12$	29.d	29.d	$7$	$162$	$27$	$22.282$		None		$2$	$0$	\(73\)	\(-5\)	\(-16687\)	\(-2111\)			$\mathrm{SU}(2)[C_{7}]$
29.12.e.a	$29$	$12$	29.e	29.e	$14$	$156$	$26$	$22.282$		None		$2$	$0$	\(-7\)	\(-7\)	\(-3749\)	\(2101\)			$\mathrm{SU}(2)[C_{14}]$
29.13.c.a	$29$	$13$	29.c	29.c	$4$	$58$	$29$	$26.506$		None		$2$	$0$	\(88\)	\(-2\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
29.14.a.a	$29$	$14$	29.a	1.a	$1$	$14$	$14$	$31.097$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2188\)	\(-67808\)	\(-669728\)	$+$	$2^{24}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-156-\beta _{1}+\beta _{3})q^{3}+(2912+\cdots)q^{4}+\cdots\)
29.14.a.b	$29$	$14$	29.a	1.a	$1$	$17$	$17$	$31.097$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(64\)	\(2186\)	\(-5308\)	\(271464\)	$-$	$2^{29}\cdot 3^{4}\cdot 7$	$\mathrm{SU}(2)$	\(q+(4-\beta _{1})q^{2}+(129-\beta _{1}+\beta _{3})q^{3}+\cdots\)
29.14.b.a	$29$	$14$	29.b	29.b	$2$	$32$	$32$	$31.097$		None		$2$	$0$	\(0\)	\(0\)	\(-90794\)	\(398260\)			$\mathrm{SU}(2)[C_{2}]$
29.15.c.a	$29$	$15$	29.c	29.c	$4$	$68$	$34$	$36.055$		None		$2$	$0$	\(-312\)	\(-2\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
29.16.a.a	$29$	$16$	29.a	1.a	$1$	$16$	$16$	$41.381$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-128\)	\(-3214\)	\(-82010\)	\(-3706320\)	$-$	$2^{33}\cdot 3^{7}\cdot 5^{4}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(-8-\beta _{1})q^{2}+(-201+\beta _{2})q^{3}+\cdots\)
29.16.a.b	$29$	$16$	29.a	1.a	$1$	$19$	$19$	$41.381$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(9908\)	\(230490\)	\(2882024\)	$+$	$2^{43}\cdot 3^{6}\cdot 5^{5}\cdot 7$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(521+2\beta _{1}+\beta _{2})q^{3}+(20389+\cdots)q^{4}+\cdots\)
29.16.b.a	$29$	$16$	29.b	29.b	$2$	$36$	$36$	$41.381$		None		$2$	$0$	\(0\)	\(0\)	\(470082\)	\(-4820620\)			$\mathrm{SU}(2)[C_{2}]$
29.17.c.a	$29$	$17$	29.c	29.c	$4$	$78$	$39$	$47.074$		None		$2$	$0$	\(184\)	\(-2\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
29.18.a.a	$29$	$18$	29.a	1.a	$1$	$18$	$18$	$53.134$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-15400\)	\(-564228\)	\(-43925040\)	$+$	$2^{42}\cdot 3^{14}\cdot 17$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-856-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
29.18.a.b	$29$	$18$	29.a	1.a	$1$	$21$	$21$	$53.134$		None	✓	$1$	$0$	\(256\)	\(23966\)	\(998272\)	\(2193368\)	$-$		$\mathrm{SU}(2)$