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 (45 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
3072.1.e.a	$3072$	$1$	3072.e	3.b	$2$	$2$	$2$	$1.533$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None	✓				768.1.i.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}-\beta q^{7}+q^{9}-\beta q^{13}+\beta q^{21}+\cdots$
3072.1.e.b	$3072$	$1$	3072.e	3.b	$2$	$2$	$2$	$1.533$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None	✓				768.1.i.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-\beta q^{7}+q^{9}+\beta q^{13}-\beta q^{21}+\cdots$
3072.1.h.a	$3072$	$1$	3072.h	24.h	$2$	$4$	$4$	$1.533$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None			✓	✓	768.1.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{13}+\cdots$
3072.1.i.a	$3072$	$1$	3072.i	48.i	$4$	$2$	$1$	$1.533$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None					1536.1.e.b	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+q^{9}+(i-1)q^{11}-2 i q^{17}+\cdots$
3072.1.i.b	$3072$	$1$	3072.i	48.i	$4$	$2$	$1$	$1.533$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None					1536.1.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}-q^{9}+(i-1)q^{11}+2 i q^{17}+\cdots$
3072.1.i.c	$3072$	$1$	3072.i	48.i	$4$	$2$	$1$	$1.533$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None					1536.1.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{3}-q^{9}+(-i+1)q^{11}+2 i q^{17}+\cdots$
3072.1.i.d	$3072$	$1$	3072.i	48.i	$4$	$2$	$1$	$1.533$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None					1536.1.e.b	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+q^{9}+(-i+1)q^{11}-2 i q^{17}+\cdots$
3072.1.i.e	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None					1536.1.e.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{8}^{3}q^{3}+(-1-\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
3072.1.i.f	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{3}) $					384.1.h.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}-\zeta_{8}^{2}q^{25}+\cdots$
3072.1.i.g	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{6}) $					192.1.h.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{19}-\zeta_{8}^{2}q^{25}+\cdots$
3072.1.i.h	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None					1536.1.e.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q+\zeta_{8}^{3}q^{3}+(1+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
3072.1.p.a	$3072$	$1$	3072.p	96.p	$8$	$8$	$2$	$1.533$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		✓			3072.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{3}+(\zeta_{16}^{5}+\zeta_{16}^{7})q^{7}+\zeta_{16}^{2}q^{9}+\cdots$
3072.1.p.b	$3072$	$1$	3072.p	96.p	$8$	$8$	$2$	$1.533$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		✓			3072.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}q^{3}+(\zeta_{16}-\zeta_{16}^{3})q^{7}+\zeta_{16}^{2}q^{9}+\cdots$
3072.1.p.c	$3072$	$1$	3072.p	96.p	$8$	$8$	$2$	$1.533$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		✓			3072.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}q^{3}+(-\zeta_{16}+\zeta_{16}^{3})q^{7}+\zeta_{16}^{2}q^{9}+\cdots$
3072.1.p.d	$3072$	$1$	3072.p	96.p	$8$	$8$	$2$	$1.533$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		✓			3072.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{3}+(-\zeta_{16}^{5}-\zeta_{16}^{7})q^{7}+\zeta_{16}^{2}q^{9}+\cdots$
3072.2.a.a	$3072$	$2$	3072.a	1.a	$1$	$2$	$2$	$24.530$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				768.2.j.b	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{7}+q^{9}+\beta q^{13}-6q^{17}+\cdots$
3072.2.a.b	$3072$	$2$	3072.a	1.a	$1$	$2$	$2$	$24.530$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1536.2.j.b	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots$
3072.2.a.c	$3072$	$2$	3072.a	1.a	$1$	$2$	$2$	$24.530$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1536.2.j.a	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{9}+4q^{11}-\beta q^{13}+\cdots$
3072.2.a.d	$3072$	$2$	3072.a	1.a	$1$	$2$	$2$	$24.530$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				768.2.j.a	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2\beta q^{5}-3\beta q^{7}+q^{9}+4q^{11}+\cdots$
3072.2.a.e	$3072$	$2$	3072.a	1.a	$1$	$2$	$2$	$24.530$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1536.2.j.a	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}-4q^{11}-\beta q^{13}+\cdots$
3072.2.a.f	$3072$	$2$	3072.a	1.a	$1$	$2$	$2$	$24.530$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				768.2.j.a	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2\beta q^{5}+3\beta q^{7}+q^{9}-4q^{11}+\cdots$
3072.2.a.g	$3072$	$2$	3072.a	1.a	$1$	$2$	$2$	$24.530$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				768.2.j.b	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{7}+q^{9}+\beta q^{13}-6q^{17}+\cdots$
3072.2.a.h	$3072$	$2$	3072.a	1.a	$1$	$2$	$2$	$24.530$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1536.2.j.b	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}-2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots$
3072.2.a.i	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	4.4.4352.1	$_{}$	None	None	✓				48.2.j.a	$1$	$1$	$0$	$-4$	$-4$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{3})q^{5}+(1+\beta _{2})q^{7}+\cdots$
3072.2.a.j	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓				1536.2.j.e	$1$	$1$	$0$	$-4$	$0$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-2-\beta _{3})q^{7}+\cdots$
3072.2.a.k	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓				1536.2.j.g	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
3072.2.a.l	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓				768.2.j.e	$2$	$0$	$0$	$-4$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots$
3072.2.a.m	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓				1536.2.j.e	$1$	$0$	$0$	$-4$	$0$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots$
3072.2.a.n	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	4.4.4352.1	$_{}$	None	None	✓				48.2.j.a	$1$	$0$	$0$	$-4$	$4$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
3072.2.a.o	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	4.4.4352.1	$_{}$	None	None	✓				48.2.j.a	$1$	$1$	$0$	$4$	$-4$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
3072.2.a.p	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓				1536.2.j.e	$1$	$1$	$0$	$4$	$0$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{3})q^{7}+\cdots$
3072.2.a.q	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓				1536.2.j.g	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
3072.2.a.r	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓				768.2.j.e	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots$
3072.2.a.s	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓				1536.2.j.e	$1$	$0$	$0$	$4$	$0$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2+\beta _{3})q^{7}+q^{9}+\cdots$
3072.2.a.t	$3072$	$2$	3072.a	1.a	$1$	$4$	$4$	$24.530$	4.4.4352.1	$_{}$	None	None	✓				48.2.j.a	$1$	$0$	$0$	$4$	$4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{3})q^{5}+(1+\beta _{2})q^{7}+q^{9}+\cdots$
3072.2.d.a	$3072$	$2$	3072.d	8.b	$2$	$4$	$4$	$24.530$	$\Q(\zeta_{8})$	$_{}$	None	None					768.2.j.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}-\beta_{3} q^{7}-q^{9}-\beta_{2} q^{13}+\cdots$
3072.2.d.b	$3072$	$2$	3072.d	8.b	$2$	$4$	$4$	$24.530$	$\Q(\zeta_{8})$	$_{}$	None	None					1536.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}-\beta_{2} q^{5}-q^{9}+4\beta_1 q^{11}+\cdots$
3072.2.d.c	$3072$	$2$	3072.d	8.b	$2$	$4$	$4$	$24.530$	$\Q(\zeta_{8})$	$_{}$	None	None					1536.2.j.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}+\beta_{2} q^{5}+2\beta_{3} q^{7}-q^{9}+\cdots$
3072.2.d.d	$3072$	$2$	3072.d	8.b	$2$	$4$	$4$	$24.530$	$\Q(\zeta_{8})$	$_{}$	None	None					768.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+2\beta_{2} q^{5}+3\beta_{3} q^{7}-q^{9}+\cdots$
3072.2.d.e	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	$\Q(\zeta_{16})$	$_{}$	None	None					1536.2.j.e	$2$	$0$	$0$	$0$	$0$	$-16$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+(-\beta_{3}+\beta_{2})q^{5}+(\beta_{5}-2)q^{7}+\cdots$
3072.2.d.f	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	8.0.18939904.2	$_{}$	None	None					48.2.j.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
3072.2.d.g	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	8.0.40960000.1	$_{}$	None	None					1536.2.j.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{2}-\beta _{7})q^{7}-q^{9}+\cdots$
3072.2.d.h	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	$\Q(\zeta_{24})$	$_{}$	None	None					768.2.j.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+(-\beta_{7}-\beta_{2})q^{5}+\beta_{3} q^{7}+\cdots$
3072.2.d.i	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	8.0.18939904.2	$_{}$	None	None					48.2.j.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(1-\beta _{1})q^{7}+\cdots$
3072.2.d.j	$3072$	$2$	3072.d	8.b	$2$	$8$	$8$	$24.530$	$\Q(\zeta_{16})$	$_{}$	None	None					1536.2.j.e	$2$	$0$	$0$	$0$	$0$	$16$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}+(-\beta_{3}+\beta_{2})q^{5}+(-\beta_{5}+2)q^{7}+\cdots$

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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.