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 80 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
1408.1.b.a	$1408$	$1$	1408.b	88.b	$2$	$1$	$1$	$0.703$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{11}) $	✓	✓			1408.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}-q^{11}+2q^{19}+q^{25}-2q^{43}+\cdots$
1408.1.b.b	$1408$	$1$	1408.b	88.b	$2$	$1$	$1$	$0.703$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{11}) $	✓	✓			1408.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+q^{11}-2q^{19}+q^{25}+2q^{43}+\cdots$
1408.1.t.a	$1408$	$1$	1408.t	88.l	$10$	$8$	$2$	$0.703$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	1408.1.t.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{20}-\zeta_{20}^{3})q^{3}+(\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{9}+\cdots$
1408.1.x.a	$1408$	$1$	1408.x	88.p	$10$	$4$	$1$	$0.703$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		✓			1408.1.x.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{10}^{2}-\zeta_{10}^{4})q^{3}+(\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{9}+\cdots$
1408.1.x.b	$1408$	$1$	1408.x	88.p	$10$	$4$	$1$	$0.703$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		✓			1408.1.x.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+(\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{9}+\cdots$
1408.2.a.a	$1408$	$2$	1408.a	1.a	$1$	$1$	$1$	$11.243$	$\Q$	$_{}$	None	None	✓	✓			1408.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-3q^{9}-q^{11}+6q^{17}+\cdots$
1408.2.a.b	$1408$	$2$	1408.a	1.a	$1$	$1$	$1$	$11.243$	$\Q$	$_{}$	None	None	✓	✓			1408.2.a.a	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-3q^{9}+q^{11}+6q^{17}+\cdots$
1408.2.a.c	$1408$	$2$	1408.a	1.a	$1$	$1$	$1$	$11.243$	$\Q$	$_{}$	None	None	✓	✓			1408.2.a.a	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-3q^{9}+q^{11}+6q^{17}+\cdots$
1408.2.a.d	$1408$	$2$	1408.a	1.a	$1$	$1$	$1$	$11.243$	$\Q$	$_{}$	None	None	✓	✓			1408.2.a.a	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-3q^{9}-q^{11}+6q^{17}+\cdots$
1408.2.a.e	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			1408.2.a.e	$1$	$1$	$0$	$-2$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-3q^{5}+\beta q^{7}+(4-2\beta )q^{9}+\cdots$
1408.2.a.f	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1408.2.a.f	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-1+2\beta )q^{5}-\beta q^{7}+\cdots$
1408.2.a.g	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1408.2.a.g	$1$	$1$	$0$	$-2$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}+(2-\beta )q^{7}-2\beta q^{9}+\cdots$
1408.2.a.h	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1408.2.a.g	$1$	$1$	$0$	$-2$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+(-2+\beta )q^{7}+\cdots$
1408.2.a.i	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1408.2.a.f	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1-2\beta )q^{5}+\beta q^{7}+\cdots$
1408.2.a.j	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			1408.2.a.e	$1$	$0$	$0$	$-2$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+3q^{5}-\beta q^{7}+(4-2\beta )q^{9}+\cdots$
1408.2.a.k	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			1408.2.a.e	$1$	$0$	$0$	$2$	$-6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-3q^{5}+\beta q^{7}+(4+2\beta )q^{9}+\cdots$
1408.2.a.l	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1408.2.a.g	$1$	$1$	$0$	$2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+(-2-\beta )q^{7}+2\beta q^{9}+\cdots$
1408.2.a.m	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1408.2.a.f	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-2\beta )q^{5}-\beta q^{7}+\cdots$
1408.2.a.n	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1408.2.a.f	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+2\beta )q^{5}+\beta q^{7}+2\beta q^{9}+\cdots$
1408.2.a.o	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1408.2.a.g	$1$	$0$	$0$	$2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(2+\beta )q^{7}+2\beta q^{9}+\cdots$
1408.2.a.p	$1408$	$2$	1408.a	1.a	$1$	$2$	$2$	$11.243$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			1408.2.a.e	$1$	$0$	$0$	$2$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+3q^{5}-\beta q^{7}+(4+2\beta )q^{9}+\cdots$
1408.2.a.q	$1408$	$2$	1408.a	1.a	$1$	$3$	$3$	$11.243$	3.3.568.1	$_{}$	None	None	✓	✓	✓		1408.2.a.q	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1408.2.a.r	$1408$	$2$	1408.a	1.a	$1$	$3$	$3$	$11.243$	3.3.568.1	$_{}$	None	None	✓	✓	✓		1408.2.a.q	$1$	$0$	$0$	$-2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
1408.2.a.s	$1408$	$2$	1408.a	1.a	$1$	$3$	$3$	$11.243$	3.3.568.1	$_{}$	None	None	✓	✓			1408.2.a.q	$1$	$0$	$0$	$2$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
1408.2.a.t	$1408$	$2$	1408.a	1.a	$1$	$3$	$3$	$11.243$	3.3.568.1	$_{}$	None	None	✓	✓			1408.2.a.q	$1$	$0$	$0$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$
1408.2.c.a	$1408$	$2$	1408.c	8.b	$2$	$4$	$4$	$11.243$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1408.2.c.a	$2$	$0$	$0$	$0$	$0$	$-12$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{3}+(-\beta_{2}+2\beta_1)q^{5}+(\beta_{3}-3)q^{7}+\cdots$
1408.2.c.b	$1408$	$2$	1408.c	8.b	$2$	$4$	$4$	$11.243$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1408.2.c.a	$2$	$0$	$0$	$0$	$0$	$12$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{3}+(-\beta_{2}-2\beta_1)q^{5}+(\beta_{3}+3)q^{7}+\cdots$
1408.2.c.c	$1408$	$2$	1408.c	8.b	$2$	$6$	$6$	$11.243$	6.0.3534400.1	$_{}$	None	None		✓			1408.2.c.c	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+\beta _{5}q^{5}+(-1-\beta _{3})q^{7}+(-2+\cdots)q^{9}+\cdots$
1408.2.c.d	$1408$	$2$	1408.c	8.b	$2$	$6$	$6$	$11.243$	6.0.3534400.1	$_{}$	None	None		✓			1408.2.c.c	$2$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-\beta _{5}q^{5}+(1+\beta _{3})q^{7}+(-2+\cdots)q^{9}+\cdots$
1408.2.c.e	$1408$	$2$	1408.c	8.b	$2$	$8$	$8$	$11.243$	8.0.18939904.2	$_{}$	None	None		✓			1408.2.c.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{4}-\beta _{5})q^{3}-\beta _{7}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
1408.2.c.f	$1408$	$2$	1408.c	8.b	$2$	$12$	$12$	$11.243$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		1408.2.c.f	$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{4}+\beta _{11})q^{3}-\beta _{6}q^{5}+\beta _{2}q^{7}+(-2+\cdots)q^{9}+\cdots$
1408.2.e.a	$1408$	$2$	1408.e	44.c	$2$	$12$	$12$	$11.243$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1408.2.e.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{3}+\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$
1408.2.e.b	$1408$	$2$	1408.e	44.c	$2$	$12$	$12$	$11.243$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1408.2.e.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{3}-\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$
1408.2.e.c	$1408$	$2$	1408.e	44.c	$2$	$12$	$12$	$11.243$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1408.2.e.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{3}-\beta _{1}q^{5}+(1+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$
1408.2.e.d	$1408$	$2$	1408.e	44.c	$2$	$12$	$12$	$11.243$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1408.2.e.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$
1408.2.g.a	$1408$	$2$	1408.g	88.g	$2$	$4$	$4$	$11.243$	$\Q(\sqrt{-2}, \sqrt{-7})$	$_{}$	None	None		✓			1408.2.g.a	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{3}q^{5}+\beta _{1}q^{7}-2q^{9}+(3-\beta _{2}+\cdots)q^{11}+\cdots$
1408.2.g.b	$1408$	$2$	1408.g	88.g	$2$	$4$	$4$	$11.243$	$\Q(\sqrt{2}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-22}) $	None		✓			1408.2.g.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}-2\beta _{1}q^{19}+\cdots$
1408.2.g.c	$1408$	$2$	1408.g	88.g	$2$	$4$	$4$	$11.243$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			1408.2.g.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta_{2}-\beta_1)q^{3}+5 q^{9}+(-2\beta_{2}+\beta_1)q^{11}+\cdots$
1408.2.g.d	$1408$	$2$	1408.g	88.g	$2$	$4$	$4$	$11.243$	$\Q(\sqrt{-2}, \sqrt{-7})$	$_{}$	None	None		✓			1408.2.g.a	$4$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}-2q^{9}+(-3+\cdots)q^{11}+\cdots$
1408.2.g.e	$1408$	$2$	1408.g	88.g	$2$	$8$	$8$	$11.243$	$\Q(\sqrt{2}, \sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			1408.2.g.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{7}q^{7}+2q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1408.2.g.f	$1408$	$2$	1408.g	88.g	$2$	$12$	$12$	$11.243$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1408.2.g.f	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{10}q^{5}+(-1+\beta _{3})q^{7}+\cdots$
1408.2.g.g	$1408$	$2$	1408.g	88.g	$2$	$12$	$12$	$11.243$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1408.2.g.f	$4$	$0$	$0$	$0$	$0$	$8$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{10}q^{5}+(1-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
1408.2.i.a	$1408$	$2$	1408.i	176.i	$4$	$44$	$22$	$11.243$		$_{}$	None	None					176.2.i.a	$4$	$0$	$0$	$-4$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
1408.2.i.b	$1408$	$2$	1408.i	176.i	$4$	$44$	$22$	$11.243$		$_{}$	None	None					176.2.i.a	$4$	$0$	$0$	$4$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
1408.2.j.a	$1408$	$2$	1408.j	16.e	$4$	$40$	$20$	$11.243$		$_{}$	None	None					176.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1408.2.j.b	$1408$	$2$	1408.j	16.e	$4$	$40$	$20$	$11.243$		$_{}$	None	None					176.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1408.3.b.a	$1408$	$3$	1408.b	88.b	$2$	$2$	$2$	$38.365$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		✓			1408.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta q^{3}-23q^{9}+(-7-3\beta )q^{11}+\cdots$
1408.3.b.b	$1408$	$3$	1408.b	88.b	$2$	$2$	$2$	$38.365$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		✓			1408.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta q^{3}-23q^{9}+(7-3\beta )q^{11}-12\beta q^{17}+\cdots$
1408.3.b.c	$1408$	$3$	1408.b	88.b	$2$	$2$	$2$	$38.365$	$\Q(\sqrt{22}) $	$_{}$	$\Q(\sqrt{-22}) $	None	✓	✓			1408.3.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{9}-11q^{11}-\beta q^{13}+6q^{19}+\cdots$
1408.3.b.d	$1408$	$3$	1408.b	88.b	$2$	$2$	$2$	$38.365$	$\Q(\sqrt{22}) $	$_{}$	$\Q(\sqrt{-22}) $	None	✓	✓			1408.3.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{9}+11q^{11}+\beta q^{13}-6q^{19}+\cdots$

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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.