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 (19 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.b	$1$	$19.563$	$\Q$	None	$-1$	$-3$	$0$	$0$	$+$	$+$	$+$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.c	$1$	$19.563$	$\Q$	None	$-1$	$-3$	$0$	$0$	$+$	$-$	$-$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.g	$1$	$19.563$	$\Q$	None	$-1$	$-1$	$0$	$0$	$+$	$-$	$-$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots$
2450.2.a.i	$1$	$19.563$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots$
2450.2.a.j	$1$	$19.563$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$q-q^{2}+q^{4}-q^{8}-3q^{9}+3q^{11}-5q^{13}+\cdots$
2450.2.a.o	$1$	$19.563$	$\Q$	None	$-1$	$2$	$0$	$0$	$+$	$-$	$-$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.p	$1$	$19.563$	$\Q$	None	$-1$	$2$	$0$	$0$	$+$	$+$	$+$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.s	$1$	$19.563$	$\Q$	None	$1$	$-3$	$0$	$0$	$-$	$-$	$+$	$q+q^{2}-3q^{3}+q^{4}-3q^{6}+q^{8}+6q^{9}+\cdots$
2450.2.a.t	$1$	$19.563$	$\Q$	None	$1$	$-2$	$0$	$0$	$-$	$+$	$-$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.u	$1$	$19.563$	$\Q$	None	$1$	$-2$	$0$	$0$	$-$	$+$	$-$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.v	$1$	$19.563$	$\Q$	None	$1$	$-2$	$0$	$0$	$-$	$+$	$-$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.y	$1$	$19.563$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots$
2450.2.a.ba	$1$	$19.563$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$q+q^{2}+q^{4}+q^{8}-3q^{9}+3q^{11}-5q^{13}+\cdots$
2450.2.a.bc	$1$	$19.563$	$\Q$	None	$1$	$1$	$0$	$0$	$-$	$+$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots$
2450.2.a.bd	$1$	$19.563$	$\Q$	None	$1$	$1$	$0$	$0$	$-$	$+$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots$
2450.2.a.bj	$2$	$19.563$	$\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.bk	$2$	$19.563$	$\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.bl	$2$	$19.563$	$\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.bo	$2$	$19.563$	$\Q(\sqrt{2}) $	None	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-4q^{11}+3\beta q^{13}+\cdots$

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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.b	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.c	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.g	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
2450.2.a.i	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots\)
2450.2.a.j	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}-q^{8}-3q^{9}+3q^{11}-5q^{13}+\cdots\)
2450.2.a.o	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(2\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.p	\(1\)	\(19.563\)	\(\Q\)	None	\(-1\)	\(2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.s	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(-3\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}-3q^{3}+q^{4}-3q^{6}+q^{8}+6q^{9}+\cdots\)
2450.2.a.t	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.u	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.v	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.y	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots\)
2450.2.a.ba	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}-3q^{9}+3q^{11}-5q^{13}+\cdots\)
2450.2.a.bc	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots\)
2450.2.a.bd	\(1\)	\(19.563\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots\)
2450.2.a.bj	\(2\)	\(19.563\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}-q^{9}+\cdots\)
2450.2.a.bk	\(2\)	\(19.563\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}-q^{9}+\cdots\)
2450.2.a.bl	\(2\)	\(19.563\)	\(\Q(\sqrt{6}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+3q^{9}+\cdots\)
2450.2.a.bo	\(2\)	\(19.563\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}-3q^{9}-4q^{11}+3\beta q^{13}+\cdots\)

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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.