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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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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.2.a.a	$11$	$2$	11.a	1.a	$1$	$1$	$1$	$0.088$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(-1\)	\(1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
13.2.e.a	$13$	$2$	13.e	13.e	$6$	$2$	$1$	$0.104$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
14.2.a.a	$14$	$2$	14.a	1.a	$1$	$1$	$1$	$0.112$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots\)
15.2.a.a	$15$	$2$	15.a	1.a	$1$	$1$	$1$	$0.120$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
16.2.e.a	$16$	$2$	16.e	16.e	$4$	$2$	$1$	$0.128$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
17.2.a.a	$17$	$2$	17.a	1.a	$1$	$1$	$1$	$0.136$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
17.2.d.a	$17$	$2$	17.d	17.d	$8$	$4$	$1$	$0.136$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-3\)	\(0\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
19.2.a.a	$19$	$2$	19.a	1.a	$1$	$1$	$1$	$0.152$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
19.2.e.a	$19$	$2$	19.e	19.e	$9$	$6$	$1$	$0.152$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(-6\)	\(-3\)	\(-6\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
20.2.a.a	$20$	$2$	20.a	1.a	$1$	$1$	$1$	$0.160$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
20.2.e.a	$20$	$2$	20.e	20.e	$4$	$2$	$1$	$0.160$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)
21.2.a.a	$21$	$2$	21.a	1.a	$1$	$1$	$1$	$0.168$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(-2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
21.2.e.a	$21$	$2$	21.e	7.c	$3$	$2$	$1$	$0.168$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(-1\)	\(2\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots\)
21.2.g.a	$21$	$2$	21.g	21.g	$6$	$2$	$1$	$0.168$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(1\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)
22.2.c.a	$22$	$2$	22.c	11.c	$5$	$4$	$1$	$0.176$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-1\)	\(-4\)	\(-6\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
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		$2$	$0$	\(-7\)	\(-7\)	\(-3\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
24.2.a.a	$24$	$2$	24.a	1.a	$1$	$1$	$1$	$0.192$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
24.2.d.a	$24$	$2$	24.d	8.b	$2$	$2$	$2$	$0.192$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)
24.2.f.a	$24$	$2$	24.f	24.f	$2$	$2$	$2$	$0.192$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)
25.2.d.a	$25$	$2$	25.d	25.d	$5$	$4$	$1$	$0.200$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-2\)	\(-1\)	\(-5\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
25.2.e.a	$25$	$2$	25.e	25.e	$10$	$8$	$2$	$0.200$	8.0.58140625.2	None		$2$	$0$	\(-5\)	\(-5\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots\)
26.2.a.a	$26$	$2$	26.a	1.a	$1$	$1$	$1$	$0.208$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(-3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
26.2.a.b	$26$	$2$	26.a	1.a	$1$	$1$	$1$	$0.208$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-3\)	\(-1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
26.2.b.a	$26$	$2$	26.b	13.b	$2$	$2$	$2$	$0.208$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
26.2.c.a	$26$	$2$	26.c	13.c	$3$	$2$	$1$	$0.208$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots\)
27.2.a.a	$27$	$2$	27.a	1.a	$1$	$1$	$1$	$0.216$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
27.2.e.a	$27$	$2$	27.e	27.e	$9$	$12$	$2$	$0.216$	12.0.\(\cdots\).1	None		$2$	$0$	\(-6\)	\(-6\)	\(-3\)	\(-6\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)
28.2.d.a	$28$	$2$	28.d	28.d	$2$	$2$	$2$	$0.224$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
28.2.e.a	$28$	$2$	28.e	7.c	$3$	$2$	$1$	$0.224$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
28.2.f.a	$28$	$2$	28.f	28.f	$6$	$4$	$2$	$0.224$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
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		$2$	$0$	\(-7\)	\(-7\)	\(-1\)	\(-11\)		$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)
30.2.a.a	$30$	$2$	30.a	1.a	$1$	$1$	$1$	$0.240$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
30.2.c.a	$30$	$2$	30.c	5.b	$2$	$2$	$2$	$0.240$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
30.2.e.a	$30$	$2$	30.e	15.e	$4$	$4$	$2$	$0.240$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
31.2.a.a	$31$	$2$	31.a	1.a	$1$	$2$	$2$	$0.248$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(1\)	\(-2\)	\(2\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
31.2.c.a	$31$	$2$	31.c	31.c	$3$	$4$	$2$	$0.248$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-4\)	\(2\)	\(-2\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
31.2.d.a	$31$	$2$	31.d	31.d	$5$	$4$	$1$	$0.248$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-3\)	\(1\)	\(-6\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
31.2.g.a	$31$	$2$	31.g	31.g	$15$	$16$	$2$	$0.248$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-6\)	\(-12\)	\(-3\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
32.2.a.a	$32$	$2$	32.a	1.a	$1$	$1$	$1$	$0.256$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots\)
32.2.g.a	$32$	$2$	32.g	32.g	$8$	$4$	$1$	$0.256$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
32.2.g.b	$32$	$2$	32.g	32.g	$8$	$8$	$2$	$0.256$	8.0.18939904.2	None		$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(-8\)		$2$	$\mathrm{SU}(2)[C_{8}]$	\(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots\)
33.2.a.a	$33$	$2$	33.a	1.a	$1$	$1$	$1$	$0.264$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
33.2.d.a	$33$	$2$	33.d	33.d	$2$	$2$	$2$	$0.264$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
33.2.e.a	$33$	$2$	33.e	11.c	$5$	$4$	$1$	$0.264$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-3\)	\(-1\)	\(-1\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots\)
33.2.e.b	$33$	$2$	33.e	11.c	$5$	$4$	$1$	$0.264$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-1\)	\(1\)	\(-3\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)

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