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-twist	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 (28 matches)

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Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	5	7	$q$-expansion
2450.2.a.a	$1$	$19.563$	$\Q$	None	$-1$	$-3$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.d	$1$	$19.563$	$\Q$	None	$-1$	$-2$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.e	$1$	$19.563$	$\Q$	None	$-1$	$-2$	$0$	$0$	$+$	$-$	$+$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.f	$1$	$19.563$	$\Q$	None	$-1$	$-2$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.h	$1$	$19.563$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots$
2450.2.a.k	$1$	$19.563$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{8}-3q^{9}+3q^{11}+5q^{13}+\cdots$
2450.2.a.l	$1$	$19.563$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}+q^{4}-q^{8}-3q^{9}+4q^{11}-6q^{13}+\cdots$
2450.2.a.m	$1$	$19.563$	$\Q$	None	$-1$	$1$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots$
2450.2.a.n	$1$	$19.563$	$\Q$	None	$-1$	$2$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.q	$1$	$19.563$	$\Q$	None	$-1$	$3$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.r	$1$	$19.563$	$\Q$	None	$-1$	$3$	$0$	$0$	$+$	$-$	$+$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.w	$1$	$19.563$	$\Q$	None	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots$
2450.2.a.x	$1$	$19.563$	$\Q$	None	$1$	$-1$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots$
2450.2.a.z	$1$	$19.563$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots$
2450.2.a.bb	$1$	$19.563$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{8}-3q^{9}+3q^{11}+5q^{13}+\cdots$
2450.2.a.be	$1$	$19.563$	$\Q$	None	$1$	$2$	$0$	$0$	$-$	$+$	$+$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.bf	$1$	$19.563$	$\Q$	None	$1$	$2$	$0$	$0$	$-$	$+$	$+$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.bg	$1$	$19.563$	$\Q$	None	$1$	$3$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots$
2450.2.a.bh	$1$	$19.563$	$\Q$	None	$1$	$3$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots$
2450.2.a.bi	$2$	$19.563$	$\Q(\sqrt{2}) $	None	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{8}-3q^{9}-4q^{11}+3\beta q^{13}+\cdots$
2450.2.a.bm	$2$	$19.563$	$\Q(\sqrt{7}) $	None	$-2$	$0$	$0$	$0$	$+$	$+$	$-$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+4q^{9}+\cdots$
2450.2.a.bn	$2$	$19.563$	$\Q(\sqrt{2}) $	None	$2$	$-4$	$0$	$0$	$-$	$+$	$+$	$q+q^{2}+(-2+\beta )q^{3}+q^{4}+(-2+\beta )q^{6}+\cdots$
2450.2.a.bp	$2$	$19.563$	$\Q(\sqrt{2}) $	None	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}-q^{9}+\cdots$
2450.2.a.bq	$2$	$19.563$	$\Q(\sqrt{6}) $	None	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}+3q^{9}+\cdots$
2450.2.a.br	$2$	$19.563$	$\Q(\sqrt{7}) $	None	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}+4q^{9}+\cdots$
2450.2.a.bs	$2$	$19.563$	$\Q(\sqrt{2}) $	None	$2$	$4$	$0$	$0$	$-$	$+$	$+$	$q+q^{2}+(2+\beta )q^{3}+q^{4}+(2+\beta )q^{6}+\cdots$
2450.2.a.bt	$4$	$19.563$	$\Q(\sqrt{2}, \sqrt{11})$	None	$-4$	$0$	$0$	$0$	$+$	$-$	$+$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{8}+\cdots$
2450.2.a.bu	$4$	$19.563$	$\Q(\sqrt{2}, \sqrt{11})$	None	$4$	$0$	$0$	$0$	$-$	$+$	$+$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{8}+\cdots$

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Elliptic curves over $\Q$
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Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	5	7	$q$-expansion
2450.2.a.a	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.d	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.e	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.f	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.h	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots\)
2450.2.a.k	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{8}-3q^{9}+3q^{11}+5q^{13}+\cdots\)
2450.2.a.l	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}-q^{8}-3q^{9}+4q^{11}-6q^{13}+\cdots\)
2450.2.a.m	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots\)
2450.2.a.n	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.q	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.r	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(3\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.w	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
2450.2.a.x	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
2450.2.a.z	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots\)
2450.2.a.bb	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{8}-3q^{9}+3q^{11}+5q^{13}+\cdots\)
2450.2.a.be	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.bf	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.bg	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(3\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
2450.2.a.bh	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(3\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
2450.2.a.bi	\(2\)	\(19.563\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{8}-3q^{9}-4q^{11}+3\beta q^{13}+\cdots\)
2450.2.a.bm	\(2\)	\(19.563\)	\(\Q(\sqrt{7}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+4q^{9}+\cdots\)
2450.2.a.bn	\(2\)	\(19.563\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(-4\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+(-2+\beta )q^{3}+q^{4}+(-2+\beta )q^{6}+\cdots\)
2450.2.a.bp	\(2\)	\(19.563\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}-q^{9}+\cdots\)
2450.2.a.bq	\(2\)	\(19.563\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}+3q^{9}+\cdots\)
2450.2.a.br	\(2\)	\(19.563\)	\(\Q(\sqrt{7}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}+4q^{9}+\cdots\)
2450.2.a.bs	\(2\)	\(19.563\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(4\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+(2+\beta )q^{3}+q^{4}+(2+\beta )q^{6}+\cdots\)
2450.2.a.bt	\(4\)	\(19.563\)	\(\Q(\sqrt{2}, \sqrt{11})\)	None	\(-4\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{8}+\cdots\)
2450.2.a.bu	\(4\)	\(19.563\)	\(\Q(\sqrt{2}, \sqrt{11})\)	None	\(4\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{8}+\cdots\)

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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.