LMFDB - Newform search results

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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 (49 matches)

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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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4212.2.a.a	$4212$	$2$	4212.a	1.a	$1$	$1$	$1$	$33.633$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-6q^{11}+q^{13}+3q^{17}+2q^{19}+\cdots$
4212.2.a.b	$4212$	$2$	4212.a	1.a	$1$	$1$	$1$	$33.633$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+6q^{11}+q^{13}-3q^{17}+2q^{19}+\cdots$
4212.2.a.c	$4212$	$2$	4212.a	1.a	$1$	$2$	$2$	$33.633$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(-1-\beta )q^{7}-\beta q^{11}+q^{13}+\cdots$
4212.2.a.d	$4212$	$2$	4212.a	1.a	$1$	$2$	$2$	$33.633$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}-q^{7}+3\beta q^{11}+q^{13}+4\beta q^{17}+\cdots$
4212.2.a.e	$4212$	$2$	4212.a	1.a	$1$	$2$	$2$	$33.633$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$0$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1-\beta )q^{7}+\beta q^{11}+q^{13}+\cdots$
4212.2.a.f	$4212$	$2$	4212.a	1.a	$1$	$4$	$4$	$33.633$	4.4.113688.1	None	✓	$1$	$0$	$0$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots$
4212.2.a.g	$4212$	$2$	4212.a	1.a	$1$	$4$	$4$	$33.633$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}-q^{13}+\cdots$
4212.2.a.h	$4212$	$2$	4212.a	1.a	$1$	$4$	$4$	$33.633$	4.4.113688.1	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots$
4212.2.a.i	$4212$	$2$	4212.a	1.a	$1$	$5$	$5$	$33.633$	5.5.8655345.1	None	✓	$1$	$1$	$0$	$0$	$-7$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots$
4212.2.a.j	$4212$	$2$	4212.a	1.a	$1$	$5$	$5$	$33.633$	5.5.8655345.1	None	✓	$1$	$0$	$0$	$0$	$7$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots$
4212.2.a.k	$4212$	$2$	4212.a	1.a	$1$	$6$	$6$	$33.633$	6.6.35342001.1	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$3$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+(\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots$
4212.2.a.l	$4212$	$2$	4212.a	1.a	$1$	$6$	$6$	$33.633$	6.6.232742592.1	None	✓	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(2-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
4212.2.a.m	$4212$	$2$	4212.a	1.a	$1$	$6$	$6$	$33.633$	6.6.35342001.1	None	✓	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+(-\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots$
4212.2.b.a	$4212$	$2$	4212.b	13.b	$2$	$2$	$2$	$33.633$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{5}+iq^{7}-3iq^{11}+(-3-2i)q^{13}+\cdots$
4212.2.b.b	$4212$	$2$	4212.b	13.b	$2$	$2$	$2$	$33.633$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{5}-iq^{7}-3iq^{11}+(-3+2i)q^{13}+\cdots$
4212.2.b.c	$4212$	$2$	4212.b	13.b	$2$	$2$	$2$	$33.633$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{5}-iq^{7}+3iq^{11}+(3-i)q^{13}+\cdots$
4212.2.b.d	$4212$	$2$	4212.b	13.b	$2$	$2$	$2$	$33.633$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{5}+iq^{7}+3iq^{11}+(3+i)q^{13}+\cdots$
4212.2.b.e	$4212$	$2$	4212.b	13.b	$2$	$4$	$4$	$33.633$	$\Q(i, \sqrt{21})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots$
4212.2.b.f	$4212$	$2$	4212.b	13.b	$2$	$4$	$4$	$33.633$	$\Q(i, \sqrt{21})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{1}q^{11}+(2-\beta _{1}+\cdots)q^{13}+\cdots$
4212.2.b.g	$4212$	$2$	4212.b	13.b	$2$	$12$	$12$	$33.633$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{5}-\beta _{10}q^{7}-\beta _{7}q^{11}+\beta _{5}q^{13}+\cdots$
4212.2.b.h	$4212$	$2$	4212.b	13.b	$2$	$12$	$12$	$33.633$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{5}+\beta _{10}q^{7}-\beta _{7}q^{11}+\beta _{6}q^{13}+\cdots$
4212.2.b.i	$4212$	$2$	4212.b	13.b	$2$	$16$	$16$	$33.633$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+\beta _{10}q^{7}-\beta _{3}q^{11}+\beta _{8}q^{13}+\cdots$
4212.2.i.a	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-4\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots$
4212.2.i.b	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots$
4212.2.i.c	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$0$	$0$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-\zeta_{6}q^{13}+\cdots$
4212.2.i.d	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$
4212.2.i.e	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots$
4212.2.i.f	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{7}-\zeta_{6}q^{13}-6q^{17}+\cdots$
4212.2.i.g	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{7}-\zeta_{6}q^{13}+6q^{17}+\cdots$
4212.2.i.h	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots$
4212.2.i.i	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$0$	$0$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$
4212.2.i.j	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-\zeta_{6}q^{13}+\cdots$
4212.2.i.k	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+4\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots$
4212.2.i.l	$4212$	$2$	4212.i	9.c	$3$	$2$	$1$	$33.633$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots$
4212.2.i.m	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
4212.2.i.n	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{5}+(-2+2\beta _{1}-\beta _{2}+2\beta _{3})q^{7}+\cdots$
4212.2.i.o	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{5}+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots$
4212.2.i.p	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{12}^{2}q^{5}+(1-\zeta_{12})q^{7}+(3\zeta_{12}^{2}+\cdots)q^{11}+\cdots$
4212.2.i.q	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\sqrt{-3}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}-2\beta _{2}q^{7}+(2\beta _{1}+2\beta _{3})q^{11}+\cdots$
4212.2.i.r	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\sqrt{-3}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}-2\beta _{2}q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots$
4212.2.i.s	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}+(-2+2\beta _{1}-\beta _{2}+2\beta _{3})q^{7}+\cdots$
4212.2.i.t	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{7}+(1+\cdots)q^{11}+\cdots$
4212.2.i.u	$4212$	$2$	4212.i	9.c	$3$	$4$	$2$	$33.633$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
4212.2.i.v	$4212$	$2$	4212.i	9.c	$3$	$8$	$4$	$33.633$	8.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$-3$	$-1$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3}+\beta _{4})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
4212.2.i.w	$4212$	$2$	4212.i	9.c	$3$	$8$	$4$	$33.633$	8.0.49787136.1	None		$4$	$0$	$0$	$0$	$0$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{5}-\beta _{4}q^{7}+\beta _{2}q^{11}+(1-\beta _{5}+\cdots)q^{13}+\cdots$
4212.2.i.x	$4212$	$2$	4212.i	9.c	$3$	$8$	$4$	$33.633$	8.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$3$	$-1$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{3}-\beta _{4})q^{5}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
4212.2.i.y	$4212$	$2$	4212.i	9.c	$3$	$12$	$6$	$33.633$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$-8$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{5}+(2\beta _{4}+\beta _{6}-\beta _{7})q^{7}+(\beta _{3}+\cdots)q^{11}+\cdots$
4212.3.d.a	$4212$	$3$	4212.d	3.b	$2$	$48$	$48$	$114.769$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4212.3.d.b	$4212$	$3$	4212.d	3.b	$2$	$48$	$48$	$114.769$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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Elliptic curves over $\Q$
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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.