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 (49 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
1881.1.b.a	$1881$	$1$	1881.b	627.b	$2$	$4$	$4$	$0.939$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓	✓	✓	1881.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+\cdots$
1881.1.bc.a	$1881$	$1$	1881.bc	209.h	$6$	$4$	$2$	$0.939$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	209.1.h.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{10}+\cdots$
1881.1.bv.a	$1881$	$1$	1881.bv	209.m	$10$	$4$	$1$	$0.939$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None					209.1.m.a	$4$	$0$	$0$	$0$	$2$	$3$		$1$		$q+\zeta_{10}^{4}q^{4}+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{5}+\cdots$
1881.1.bv.b	$1881$	$1$	1881.bv	209.m	$10$	$8$	$2$	$0.939$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		✓	✓		1881.1.bv.b	$8$	$0$	$0$	$0$	$0$	$-6$		$1$		$q+\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{5}+\cdots$
1881.1.by.a	$1881$	$1$	1881.by	627.y	$10$	$16$	$4$	$0.939$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		✓	✓	✓	1881.1.by.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{12}q^{4}+(-\zeta_{40}+\zeta_{40}^{7})q^{5}+\cdots$
1881.2.a.a	$1881$	$2$	1881.a	1.a	$1$	$1$	$1$	$15.020$	$\Q$	$_{}$	None	None	✓				627.2.a.b	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-4q^{5}+2q^{7}+q^{11}+q^{13}+\cdots$
1881.2.a.b	$1881$	$2$	1881.a	1.a	$1$	$1$	$1$	$15.020$	$\Q$	$_{}$	None	None	✓				627.2.a.a	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{7}-q^{11}-q^{13}+4q^{16}+\cdots$
1881.2.a.c	$1881$	$2$	1881.a	1.a	$1$	$1$	$1$	$15.020$	$\Q$	$_{}$	None	None	✓				209.2.a.a	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{5}-4q^{7}-q^{11}+2q^{13}+\cdots$
1881.2.a.d	$1881$	$2$	1881.a	1.a	$1$	$2$	$2$	$15.020$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				209.2.a.b	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{5}+(-2+\beta )q^{7}-2\beta q^{8}+\cdots$
1881.2.a.e	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				627.2.a.f	$1$	$1$	$-2$	$0$	$3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1881.2.a.f	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	3.3.169.1	$_{}$	None	None	✓				627.2.a.g	$1$	$1$	$-2$	$0$	$-5$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1881.2.a.g	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				627.2.a.d	$1$	$0$	$2$	$0$	$7$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
1881.2.a.h	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	3.3.169.1	$_{}$	None	None	✓				627.2.a.c	$1$	$1$	$2$	$0$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1881.2.a.i	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	3.3.321.1	$_{}$	None	None	✓				627.2.a.e	$1$	$0$	$2$	$0$	$3$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
1881.2.a.j	$1881$	$2$	1881.a	1.a	$1$	$4$	$4$	$15.020$	4.4.23377.1	$_{}$	None	None	✓		✓		627.2.a.h	$1$	$1$	$-1$	$0$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
1881.2.a.k	$1881$	$2$	1881.a	1.a	$1$	$5$	$5$	$15.020$	5.5.246832.1	$_{}$	None	None	✓				209.2.a.c	$1$	$0$	$-2$	$0$	$5$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots$
1881.2.a.l	$1881$	$2$	1881.a	1.a	$1$	$5$	$5$	$15.020$	5.5.2179633.1	$_{}$	None	None	✓				627.2.a.i	$1$	$0$	$-1$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots$
1881.2.a.m	$1881$	$2$	1881.a	1.a	$1$	$5$	$5$	$15.020$	5.5.1920025.1	$_{}$	None	None	✓				627.2.a.j	$1$	$0$	$-1$	$0$	$-7$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots$
1881.2.a.n	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1881.2.a.n	$1$	$1$	$-2$	$0$	$-8$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{2}+(1-\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
1881.2.a.o	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1881.2.a.o	$1$	$1$	$-2$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
1881.2.a.p	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓		✓		209.2.a.d	$1$	$0$	$1$	$0$	$-2$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\beta _{4}q^{5}+\cdots$
1881.2.a.q	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1881.2.a.o	$1$	$0$	$2$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
1881.2.a.r	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1881.2.a.n	$1$	$0$	$2$	$0$	$8$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+(1-\beta _{3})q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1881.2.f.a	$1881$	$2$	1881.f	33.d	$2$	$72$	$72$	$15.020$		$_{}$	None	None		✓	✓	✓	1881.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1881.2.g.a	$1881$	$2$	1881.g	57.d	$2$	$64$	$64$	$15.020$		$_{}$	None	None		✓	✓	✓	1881.2.g.a	$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{2}]$
1881.2.h.a	$1881$	$2$	1881.h	209.d	$2$	$2$	$2$	$15.020$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None					209.2.d.a	$4$	$1$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}-q^{5}+(-1+2\beta )q^{7}+(-2+\cdots)q^{11}+\cdots$
1881.2.h.b	$1881$	$2$	1881.h	209.d	$2$	$4$	$4$	$15.020$	$\Q(\sqrt{-11}, \sqrt{19})$	$_{}$	$\Q(\sqrt{-627}) $	None		✓			1881.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+\beta _{2}q^{11}-\beta _{1}q^{13}+4q^{16}+\cdots$
1881.2.h.c	$1881$	$2$	1881.h	209.d	$2$	$4$	$4$	$15.020$	$\Q(i, \sqrt{19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1881.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{3})q^{7}+\cdots$
1881.2.h.d	$1881$	$2$	1881.h	209.d	$2$	$8$	$8$	$15.020$	8.0.3288334336.3	$_{}$	None	None					209.2.d.b	$4$	$0$	$0$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}-\beta _{3}q^{4}+(1+\beta _{3})q^{5}+\beta _{5}q^{7}+\cdots$
1881.2.h.e	$1881$	$2$	1881.h	209.d	$2$	$8$	$8$	$15.020$	8.0.484000000.9	$_{}$	None	None					209.2.d.c	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(1+2\beta _{3})q^{4}+(-2+3\beta _{3}+\cdots)q^{5}+\cdots$
1881.2.h.f	$1881$	$2$	1881.h	209.d	$2$	$16$	$16$	$15.020$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					627.2.h.a	$4$	$0$	$0$	$0$	$4$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{11}q^{2}+(1+\beta _{10}-\beta _{15})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1881.2.h.g	$1881$	$2$	1881.h	209.d	$2$	$24$	$24$	$15.020$		$_{}$	None	None					627.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1881.2.h.h	$1881$	$2$	1881.h	209.d	$2$	$32$	$32$	$15.020$		$_{}$	None	None		✓	✓		1881.2.h.h	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1881.4.a.a	$1881$	$4$	1881.a	1.a	$1$	$8$	$8$	$110.983$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				209.4.a.a	$1$	$1$	$0$	$0$	$12$	$-59$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(2-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots$
1881.4.a.b	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓				627.4.a.b	$1$	$1$	$0$	$0$	$1$	$-4$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots$
1881.4.a.c	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓				627.4.a.d	$1$	$0$	$0$	$0$	$21$	$10$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1}-\beta _{9})q^{5}+\cdots$
1881.4.a.d	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓				627.4.a.c	$1$	$1$	$0$	$0$	$21$	$-38$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(2-\beta _{7})q^{5}+\cdots$
1881.4.a.e	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓				209.4.a.b	$1$	$1$	$6$	$0$	$10$	$-53$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
1881.4.a.f	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓				627.4.a.a	$1$	$0$	$8$	$0$	$41$	$-52$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(5+\beta _{2}+\beta _{3})q^{4}+(4+\cdots)q^{5}+\cdots$
1881.4.a.g	$1881$	$4$	1881.a	1.a	$1$	$12$	$12$	$110.983$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓		✓		627.4.a.g	$1$	$1$	$-6$	$0$	$-49$	$-18$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(-4+\beta _{4}+\cdots)q^{5}+\cdots$
1881.4.a.h	$1881$	$4$	1881.a	1.a	$1$	$12$	$12$	$110.983$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓		✓		627.4.a.h	$1$	$1$	$-6$	$0$	$-29$	$60$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(6+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
1881.4.a.i	$1881$	$4$	1881.a	1.a	$1$	$12$	$12$	$110.983$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓				627.4.a.f	$1$	$0$	$-6$	$0$	$-9$	$46$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}+\cdots$
1881.4.a.j	$1881$	$4$	1881.a	1.a	$1$	$12$	$12$	$110.983$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓				627.4.a.e	$1$	$0$	$2$	$0$	$-29$	$-4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(-2+\beta _{4})q^{5}+\cdots$
1881.4.a.k	$1881$	$4$	1881.a	1.a	$1$	$13$	$13$	$110.983$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓		✓		209.4.a.c	$1$	$0$	$2$	$0$	$-8$	$39$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(6+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots$
1881.4.a.l	$1881$	$4$	1881.a	1.a	$1$	$15$	$15$	$110.983$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓		✓		209.4.a.d	$1$	$0$	$-4$	$0$	$-10$	$73$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(-1-\beta _{6})q^{5}+\cdots$
1881.4.a.m	$1881$	$4$	1881.a	1.a	$1$	$23$	$23$	$110.983$		$_{}$	None	None	✓	✓	✓	✓	1881.4.a.m	$1$	$1$	$-4$	$0$	$-40$	$14$	$-$		$\mathrm{SU}(2)$
1881.4.a.n	$1881$	$4$	1881.a	1.a	$1$	$23$	$23$	$110.983$		$_{}$	None	None	✓	✓	✓	✓	1881.4.a.n	$1$	$1$	$-4$	$0$	$0$	$-14$	$-$		$\mathrm{SU}(2)$
1881.4.a.o	$1881$	$4$	1881.a	1.a	$1$	$23$	$23$	$110.983$		$_{}$	None	None	✓	✓	✓	✓	1881.4.a.n	$1$	$0$	$4$	$0$	$0$	$-14$	$+$		$\mathrm{SU}(2)$
1881.4.a.p	$1881$	$4$	1881.a	1.a	$1$	$23$	$23$	$110.983$		$_{}$	None	None	✓	✓	✓	✓	1881.4.a.m	$1$	$0$	$4$	$0$	$40$	$14$	$+$		$\mathrm{SU}(2)$

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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.