LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 101 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
952.1.e.a	$952$	$1$	952.e	952.e	$2$	$1$	$1$	$0.475$	$\Q$	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-238}) $	$\Q(\sqrt{2}) $	✓	✓			952.1.e.a	$4$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{9}+q^{14}+\cdots$
952.1.e.b	$952$	$1$	952.e	952.e	$2$	$1$	$1$	$0.475$	$\Q$	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-238}) $	$\Q(\sqrt{2}) $	✓	✓			952.1.e.a	$4$	$0$	$-1$	$0$	$0$	$1$		$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}-q^{14}+\cdots$
952.1.e.c	$952$	$1$	952.e	952.e	$2$	$4$	$4$	$0.475$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		✓			952.1.e.c	$4$	$0$	$1$	$0$	$0$	$4$		$1$		$q+\zeta_{10}q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
952.1.e.d	$952$	$1$	952.e	952.e	$2$	$4$	$4$	$0.475$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		✓			952.1.e.c	$4$	$0$	$1$	$0$	$0$	$-4$		$1$		$q-\zeta_{10}^{4}q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
952.1.bi.a	$952$	$1$	952.bi	952.ai	$6$	$2$	$1$	$0.475$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-34}) $	None		✓			952.1.bi.a	$4$	$0$	$-1$	$0$	$-1$	$1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots$
952.1.bi.b	$952$	$1$	952.bi	952.ai	$6$	$2$	$1$	$0.475$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-34}) $	None		✓			952.1.bi.a	$4$	$0$	$-1$	$0$	$1$	$-1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
952.1.bi.c	$952$	$1$	952.bi	952.ai	$6$	$4$	$2$	$0.475$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-34}) $	None		✓	✓		952.1.bi.c	$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
952.2.a.a	$952$	$2$	952.a	1.a	$1$	$2$	$2$	$7.602$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	952.2.a.a	$1$	$1$	$0$	$-1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots$
952.2.a.b	$952$	$2$	952.a	1.a	$1$	$2$	$2$	$7.602$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	✓	✓	952.2.a.b	$1$	$1$	$0$	$1$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{5}-q^{7}+\beta q^{9}+\cdots$
952.2.a.c	$952$	$2$	952.a	1.a	$1$	$3$	$3$	$7.602$	3.3.229.1	$_{}$	None	None	✓	✓	✓	✓	952.2.a.c	$1$	$1$	$0$	$-3$	$-5$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(-2-\beta _{2})q^{5}+q^{7}+\cdots$
952.2.a.d	$952$	$2$	952.a	1.a	$1$	$3$	$3$	$7.602$	3.3.229.1	$_{}$	None	None	✓	✓	✓	✓	952.2.a.d	$1$	$1$	$0$	$-3$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{2}q^{5}-q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots$
952.2.a.e	$952$	$2$	952.a	1.a	$1$	$3$	$3$	$7.602$	3.3.1229.1	$_{}$	None	None	✓	✓	✓	✓	952.2.a.e	$1$	$0$	$0$	$-1$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots$
952.2.a.f	$952$	$2$	952.a	1.a	$1$	$3$	$3$	$7.602$	3.3.229.1	$_{}$	None	None	✓	✓	✓	✓	952.2.a.f	$1$	$0$	$0$	$1$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}+q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots$
952.2.a.g	$952$	$2$	952.a	1.a	$1$	$4$	$4$	$7.602$	4.4.5225.1	$_{}$	None	None	✓	✓	✓	✓	952.2.a.g	$1$	$0$	$0$	$3$	$-1$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}-q^{7}+\cdots$
952.2.a.h	$952$	$2$	952.a	1.a	$1$	$4$	$4$	$7.602$	4.4.13448.1	$_{}$	None	None	✓	✓	✓	✓	952.2.a.h	$1$	$0$	$0$	$3$	$5$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(1-\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots$
952.2.b.a	$952$	$2$	952.b	8.b	$2$	$2$	$2$	$7.602$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			952.2.b.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+\beta q^{3}-2q^{4}-\beta q^{5}-2q^{6}+\cdots$
952.2.b.b	$952$	$2$	952.b	8.b	$2$	$2$	$2$	$7.602$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			952.2.b.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}-q^{7}-2\beta q^{8}+3q^{9}+\cdots$
952.2.b.c	$952$	$2$	952.b	8.b	$2$	$2$	$2$	$7.602$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			952.2.b.c	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+2\beta q^{3}-2q^{4}-2\beta q^{5}+4q^{6}+\cdots$
952.2.b.d	$952$	$2$	952.b	8.b	$2$	$16$	$16$	$7.602$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			952.2.b.d	$2$	$0$	$0$	$0$	$0$	$16$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{3}q^{3}+(1-\beta _{6})q^{4}+\beta _{11}q^{5}+\cdots$
952.2.b.e	$952$	$2$	952.b	8.b	$2$	$16$	$16$	$7.602$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			952.2.b.e	$2$	$0$	$1$	$0$	$0$	$-16$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{8}q^{3}-\beta _{4}q^{4}+\beta _{12}q^{5}+\cdots$
952.2.b.f	$952$	$2$	952.b	8.b	$2$	$28$	$28$	$7.602$		$_{}$	None	None		✓			952.2.b.f	$2$	$0$	$1$	$0$	$0$	$-28$			$\mathrm{SU}(2)[C_{2}]$
952.2.b.g	$952$	$2$	952.b	8.b	$2$	$30$	$30$	$7.602$		$_{}$	None	None		✓	✓		952.2.b.g	$2$	$0$	$0$	$0$	$0$	$30$			$\mathrm{SU}(2)[C_{2}]$
952.2.c.a	$952$	$2$	952.c	17.b	$2$	$2$	$2$	$7.602$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			952.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}+2 i q^{5}-i q^{7}-q^{9}+2 i q^{11}+\cdots$
952.2.c.b	$952$	$2$	952.c	17.b	$2$	$4$	$4$	$7.602$	$\Q(i, \sqrt{29})$	$_{}$	None	None		✓			952.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+\cdots$
952.2.c.c	$952$	$2$	952.c	17.b	$2$	$4$	$4$	$7.602$	$\Q(i, \sqrt{13})$	$_{}$	None	None		✓			952.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+(-4+\cdots)q^{9}+\cdots$
952.2.c.d	$952$	$2$	952.c	17.b	$2$	$8$	$8$	$7.602$	8.0.6179217664.1	$_{}$	None	None		✓			952.2.c.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{5}-\beta _{6})q^{3}+(-\beta _{5}-\beta _{7})q^{5}+\cdots$
952.2.c.e	$952$	$2$	952.c	17.b	$2$	$10$	$10$	$7.602$	10.0.$\cdots$.1	$_{}$	None	None		✓	✓		952.2.c.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{3}+(\beta _{4}+\beta _{6}+\beta _{7}-\beta _{8}-\beta _{9})q^{5}+\cdots$
952.2.i.a	$952$	$2$	952.i	56.e	$2$	$128$	$128$	$7.602$		$_{}$	None	None		✓	✓	✓	952.2.i.a	$4$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
952.2.k.a	$952$	$2$	952.k	952.k	$2$	$8$	$8$	$7.602$	8.0.5473632256.3	$_{}$	$\Q(\sqrt{-34}) $	None		✓			952.2.k.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{2}+2q^{4}+(-\beta _{1}-\beta _{6})q^{5}+\beta _{4}q^{7}+\cdots$
952.2.k.b	$952$	$2$	952.k	952.k	$2$	$20$	$20$	$7.602$	20.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-119}) $	None		✓			952.2.k.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{5}q^{2}+\beta _{13}q^{3}+\beta _{8}q^{4}+(-\beta _{10}+\cdots)q^{5}+\cdots$
952.2.k.c	$952$	$2$	952.k	952.k	$2$	$112$	$112$	$7.602$		$_{}$	None	None		✓	✓		952.2.k.c	$8$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
952.2.p.a	$952$	$2$	952.p	136.h	$2$	$108$	$108$	$7.602$		$_{}$	None	None		✓	✓	✓	952.2.p.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
952.2.q.a	$952$	$2$	952.q	7.c	$3$	$2$	$1$	$7.602$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			952.2.q.a	$2$	$0$	$0$	$0$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
952.2.q.b	$952$	$2$	952.q	7.c	$3$	$2$	$1$	$7.602$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			952.2.q.b	$2$	$0$	$0$	$3$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
952.2.q.c	$952$	$2$	952.q	7.c	$3$	$12$	$6$	$7.602$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			952.2.q.c	$2$	$0$	$0$	$-1$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}-\beta _{11}q^{5}+(\beta _{2}-\beta _{6}-\beta _{9}+\cdots)q^{7}+\cdots$
952.2.q.d	$952$	$2$	952.q	7.c	$3$	$14$	$7$	$7.602$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			952.2.q.d	$2$	$0$	$0$	$0$	$1$	$-7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(\beta _{3}-\beta _{10})q^{5}+(-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$
952.2.q.e	$952$	$2$	952.q	7.c	$3$	$14$	$7$	$7.602$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			952.2.q.e	$2$	$0$	$0$	$3$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}-\beta _{13}q^{5}+(\beta _{4}-\beta _{7}+\beta _{10}+\cdots)q^{7}+\cdots$
952.2.q.f	$952$	$2$	952.q	7.c	$3$	$20$	$10$	$7.602$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		952.2.q.f	$2$	$0$	$0$	$-1$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2})q^{3}+\beta _{12}q^{5}+\beta _{18}q^{7}+\cdots$
952.2.s.a	$952$	$2$	952.s	136.i	$4$	$216$	$108$	$7.602$		$_{}$	None	None		✓	✓	✓	952.2.s.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
952.2.w.a	$952$	$2$	952.w	17.c	$4$	$24$	$12$	$7.602$		$_{}$	None	None		✓			952.2.w.a	$2$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
952.2.w.b	$952$	$2$	952.w	17.c	$4$	$32$	$16$	$7.602$		$_{}$	None	None		✓	✓		952.2.w.b	$2$	$0$	$0$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
952.2.x.a	$952$	$2$	952.x	952.x	$4$	$280$	$140$	$7.602$		$_{}$	None	None		✓	✓	✓	952.2.x.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
952.2.z.a	$952$	$2$	952.z	952.z	$6$	$4$	$2$	$7.602$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			952.2.z.a	$4$	$0$	$2$	$-4$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+2\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
952.2.z.b	$952$	$2$	952.z	952.z	$6$	$4$	$2$	$7.602$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			952.2.z.a	$4$	$0$	$2$	$4$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(2-2\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
952.2.z.c	$952$	$2$	952.z	952.z	$6$	$272$	$136$	$7.602$		$_{}$	None	None		✓	✓		952.2.z.c	$8$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
952.2.bf.a	$952$	$2$	952.bf	952.af	$6$	$16$	$8$	$7.602$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-34}) $	None		✓			952.2.bf.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 7$	$\mathrm{U}(1)[D_{6}]$	$q+(\beta _{2}+\beta _{6})q^{2}-2\beta _{5}q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
952.2.bf.b	$952$	$2$	952.bf	952.af	$6$	$264$	$132$	$7.602$		$_{}$	None	None		✓	✓		952.2.bf.b	$8$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
952.2.bh.a	$952$	$2$	952.bh	56.m	$6$	$256$	$128$	$7.602$		$_{}$	None	None		✓	✓	✓	952.2.bh.a	$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
952.2.bm.a	$952$	$2$	952.bm	56.p	$6$	$4$	$2$	$7.602$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			952.2.bm.a	$2$	$1$	$0$	$-6$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$
952.2.bm.b	$952$	$2$	952.bm	56.p	$6$	$4$	$2$	$7.602$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			952.2.bm.a	$2$	$0$	$0$	$6$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.