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 (1-50 of 58 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2088.1.b.a	$2088$	$1$	2088.b	232.b	$2$	$1$	$1$	$1.042$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-58}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{16}+q^{25}+q^{29}+\cdots$
2088.1.b.b	$2088$	$1$	2088.b	232.b	$2$	$1$	$1$	$1.042$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-58}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}+q^{25}-q^{29}+\cdots$
2088.1.b.c	$2088$	$1$	2088.b	232.b	$2$	$2$	$2$	$1.042$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
2088.1.b.d	$2088$	$1$	2088.b	232.b	$2$	$2$	$2$	$1.042$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
2088.1.y.a	$2088$	$1$	2088.y	232.l	$4$	$4$	$2$	$1.042$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
2088.1.bb.a	$2088$	$1$	2088.bb	2088.ab	$6$	$4$	$2$	$1.042$	$\Q(\zeta_{12})$	$D_{6}$	None	$\Q(\sqrt{58}) $		$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+q^{6}+\cdots$
2088.1.cn.a	$2088$	$1$	2088.cn	232.u	$28$	$24$	$2$	$1.042$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{56}^{5}q^{2}+\zeta_{56}^{10}q^{4}+(-\zeta_{56}^{3}+\cdots)q^{5}+\cdots$
2088.2.a.a	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+3q^{7}-q^{11}+q^{13}+q^{17}+\cdots$
2088.2.a.b	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}+2q^{13}-6q^{17}+4q^{23}+\cdots$
2088.2.a.c	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+2q^{11}+4q^{13}-5q^{17}+\cdots$
2088.2.a.d	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{11}-q^{13}-4q^{23}+\cdots$
2088.2.a.e	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-5q^{7}+5q^{11}+q^{13}+3q^{17}-4q^{19}+\cdots$
2088.2.a.f	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{11}+q^{13}+7q^{17}-6q^{19}+\cdots$
2088.2.a.g	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+3q^{11}+q^{13}-7q^{17}-6q^{19}+\cdots$
2088.2.a.h	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+3q^{11}+q^{13}+q^{17}+6q^{23}+\cdots$
2088.2.a.i	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+2q^{13}+6q^{17}-4q^{23}+\cdots$
2088.2.a.j	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+3q^{11}-7q^{13}-3q^{17}+\cdots$
2088.2.a.k	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+3q^{7}+5q^{11}+q^{13}+7q^{17}+\cdots$
2088.2.a.l	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}+2q^{11}+4q^{13}-7q^{17}+\cdots$
2088.2.a.m	$2088$	$2$	2088.a	1.a	$1$	$1$	$1$	$16.673$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}+3q^{11}-5q^{13}+4q^{17}+\cdots$
2088.2.a.n	$2088$	$2$	2088.a	1.a	$1$	$2$	$2$	$16.673$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+(1+\beta )q^{7}+(-3+\beta )q^{11}+\cdots$
2088.2.a.o	$2088$	$2$	2088.a	1.a	$1$	$2$	$2$	$16.673$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}-q^{7}+(-1+\beta )q^{11}+(-3+\cdots)q^{13}+\cdots$
2088.2.a.p	$2088$	$2$	2088.a	1.a	$1$	$2$	$2$	$16.673$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(1-\beta )q^{11}+(-3+\beta )q^{13}+\cdots$
2088.2.a.q	$2088$	$2$	2088.a	1.a	$1$	$2$	$2$	$16.673$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+2\beta )q^{5}-4q^{7}+(1+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots$
2088.2.a.r	$2088$	$2$	2088.a	1.a	$1$	$2$	$2$	$16.673$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(1-2\beta )q^{7}+(-2-\beta )q^{11}+\cdots$
2088.2.a.s	$2088$	$2$	2088.a	1.a	$1$	$3$	$3$	$16.673$	3.3.568.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+(-1-\beta _{1}-2\beta _{2})q^{11}+\cdots$
2088.2.a.t	$2088$	$2$	2088.a	1.a	$1$	$3$	$3$	$16.673$	3.3.961.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(1-\beta _{2})q^{7}+(-1+\beta _{1}-\beta _{2})q^{11}+\cdots$
2088.2.a.u	$2088$	$2$	2088.a	1.a	$1$	$3$	$3$	$16.673$	3.3.892.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$9$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+3q^{7}+(-1+\beta _{2})q^{11}+(1+\cdots)q^{13}+\cdots$
2088.2.a.v	$2088$	$2$	2088.a	1.a	$1$	$3$	$3$	$16.673$	3.3.892.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$9$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+3q^{7}+(1-\beta _{2})q^{11}+(1+\beta _{2})q^{13}+\cdots$
2088.2.o.a	$2088$	$2$	2088.o	29.b	$2$	$2$	$2$	$16.673$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-5q^{7}-iq^{11}+3q^{13}-3iq^{17}+\cdots$
2088.2.o.b	$2088$	$2$	2088.o	29.b	$2$	$2$	$2$	$16.673$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4iq^{11}-2q^{13}+2iq^{17}-4iq^{19}+\cdots$
2088.2.o.c	$2088$	$2$	2088.o	29.b	$2$	$4$	$4$	$16.673$	$\Q(i, \sqrt{33})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$12$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{3})q^{5}+3q^{7}+(\beta _{1}+4\beta _{2})q^{11}+\cdots$
2088.2.o.d	$2088$	$2$	2088.o	29.b	$2$	$6$	$6$	$16.673$	6.0.59105344.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-6$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{5}-q^{7}+(\beta _{2}-\beta _{3})q^{11}+(2-\beta _{4}+\cdots)q^{13}+\cdots$
2088.2.o.e	$2088$	$2$	2088.o	29.b	$2$	$8$	$8$	$16.673$	8.0.4589249536.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{5}+(1-\beta _{6})q^{7}-\beta _{1}q^{11}+(-1+\cdots)q^{13}+\cdots$
2088.2.o.f	$2088$	$2$	2088.o	29.b	$2$	$16$	$16$	$16.673$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{14}q^{5}-\beta _{12}q^{7}+\beta _{2}q^{11}-\beta _{8}q^{13}+\cdots$
2088.2.x.a	$2088$	$2$	2088.x	87.f	$4$	$28$	$14$	$16.673$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
2088.2.x.b	$2088$	$2$	2088.x	87.f	$4$	$32$	$16$	$16.673$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
2088.3.g.a	$2088$	$3$	2088.g	3.b	$2$	$28$	$28$	$56.894$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-32$			$\mathrm{SU}(2)[C_{2}]$
2088.3.g.b	$2088$	$3$	2088.g	3.b	$2$	$28$	$28$	$56.894$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2088.3.i.a	$2088$	$3$	2088.i	87.d	$2$	$4$	$4$	$56.894$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$16$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(3\zeta_{8}+3\zeta_{8}^{3})q^{5}+4q^{7}+(4\zeta_{8}-4\zeta_{8}^{3})q^{11}+\cdots$
2088.3.i.b	$2088$	$3$	2088.i	87.d	$2$	$56$	$56$	$56.894$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-32$			$\mathrm{SU}(2)[C_{2}]$
2088.4.a.a	$2088$	$4$	2088.a	1.a	$1$	$3$	$3$	$123.196$	3.3.4481.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-11$	$-38$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-4-\beta _{1}-\beta _{2})q^{5}+(-13+\beta _{1}+\cdots)q^{7}+\cdots$
2088.4.a.b	$2088$	$4$	2088.a	1.a	$1$	$3$	$3$	$123.196$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$16$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-3\beta _{1}+4\beta _{2})q^{5}+(2+2\beta _{1}+\cdots)q^{7}+\cdots$
2088.4.a.c	$2088$	$4$	2088.a	1.a	$1$	$4$	$4$	$123.196$	4.4.6020961.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-22$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{5}+(-5-\beta _{1})q^{7}+(9+\cdots)q^{11}+\cdots$
2088.4.a.d	$2088$	$4$	2088.a	1.a	$1$	$4$	$4$	$123.196$	4.4.518057.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$11$	$-6$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(3+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$
2088.4.a.e	$2088$	$4$	2088.a	1.a	$1$	$4$	$4$	$123.196$	4.4.225792.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$20$	$-8$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(5-\beta _{2})q^{5}+(-2-2\beta _{1}-\beta _{2}+2\beta _{3})q^{7}+\cdots$
2088.4.a.f	$2088$	$4$	2088.a	1.a	$1$	$5$	$5$	$123.196$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-10$	$32$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{3})q^{5}+(6+\beta _{2}+\beta _{4})q^{7}+\cdots$
2088.4.a.g	$2088$	$4$	2088.a	1.a	$1$	$5$	$5$	$123.196$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-9$	$-6$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+(12+\cdots)q^{11}+\cdots$
2088.4.a.h	$2088$	$4$	2088.a	1.a	$1$	$5$	$5$	$123.196$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$19$	$10$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(4-\beta _{2})q^{5}+(2-\beta _{3}+\beta _{4})q^{7}+(-1+\cdots)q^{11}+\cdots$
2088.4.a.i	$2088$	$4$	2088.a	1.a	$1$	$6$	$6$	$123.196$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-16$	$-11$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-3+\beta _{2})q^{5}+(-2+\beta _{4})q^{7}+(-8+\cdots)q^{11}+\cdots$

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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.