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 (32 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
3920.2.a.b	$1$	$31.301$	$\Q$	None	$0$	$-3$	$-1$	$0$	$-$	$+$	$+$	$q-3q^{3}-q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots$
3920.2.a.c	$1$	$31.301$	$\Q$	None	$0$	$-3$	$-1$	$0$	$+$	$+$	$-$	$q-3q^{3}-q^{5}+6q^{9}+5q^{11}+5q^{13}+\cdots$
3920.2.a.d	$1$	$31.301$	$\Q$	None	$0$	$-3$	$1$	$0$	$-$	$-$	$-$	$q-3q^{3}+q^{5}+6q^{9}+2q^{11}+6q^{13}+\cdots$
3920.2.a.g	$1$	$31.301$	$\Q$	None	$0$	$-2$	$1$	$0$	$-$	$-$	$-$	$q-2q^{3}+q^{5}+q^{9}-3q^{11}-5q^{13}+\cdots$
3920.2.a.h	$1$	$31.301$	$\Q$	None	$0$	$-2$	$1$	$0$	$-$	$-$	$-$	$q-2q^{3}+q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
3920.2.a.j	$1$	$31.301$	$\Q$	None	$0$	$-2$	$1$	$0$	$-$	$-$	$-$	$q-2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
3920.2.a.k	$1$	$31.301$	$\Q$	None	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$q-q^{3}-q^{5}-2q^{9}-6q^{11}+2q^{13}+\cdots$
3920.2.a.l	$1$	$31.301$	$\Q$	None	$0$	$-1$	$-1$	$0$	$+$	$+$	$-$	$q-q^{3}-q^{5}-2q^{9}-3q^{11}-q^{13}+\cdots$
3920.2.a.o	$1$	$31.301$	$\Q$	None	$0$	$-1$	$-1$	$0$	$+$	$+$	$-$	$q-q^{3}-q^{5}-2q^{9}+5q^{11}+7q^{13}+\cdots$
3920.2.a.p	$1$	$31.301$	$\Q$	None	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$q-q^{3}-q^{5}-2q^{9}+6q^{11}-4q^{13}+\cdots$
3920.2.a.s	$1$	$31.301$	$\Q$	None	$0$	$0$	$-1$	$0$	$+$	$+$	$-$	$q-q^{5}-3q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots$
3920.2.a.t	$1$	$31.301$	$\Q$	None	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$q+q^{5}-3q^{9}-4q^{11}+6q^{13}-2q^{17}+\cdots$
3920.2.a.w	$1$	$31.301$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{5}-2q^{9}-6q^{11}-2q^{13}+\cdots$
3920.2.a.z	$1$	$31.301$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{5}-2q^{9}+q^{11}+5q^{13}+\cdots$
3920.2.a.ba	$1$	$31.301$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{5}-2q^{9}+3q^{11}-5q^{13}+\cdots$
3920.2.a.bc	$1$	$31.301$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{5}-2q^{9}+6q^{11}+4q^{13}+\cdots$
3920.2.a.bd	$1$	$31.301$	$\Q$	None	$0$	$2$	$-1$	$0$	$+$	$+$	$-$	$q+2q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
3920.2.a.be	$1$	$31.301$	$\Q$	None	$0$	$2$	$-1$	$0$	$-$	$+$	$+$	$q+2q^{3}-q^{5}+q^{9}-3q^{11}+5q^{13}+\cdots$
3920.2.a.bi	$1$	$31.301$	$\Q$	None	$0$	$3$	$-1$	$0$	$-$	$+$	$+$	$q+3q^{3}-q^{5}+6q^{9}+2q^{11}-6q^{13}+\cdots$
3920.2.a.bj	$1$	$31.301$	$\Q$	None	$0$	$3$	$1$	$0$	$-$	$-$	$-$	$q+3q^{3}+q^{5}+6q^{9}-q^{11}-3q^{13}+\cdots$
3920.2.a.bk	$1$	$31.301$	$\Q$	None	$0$	$3$	$1$	$0$	$-$	$-$	$-$	$q+3q^{3}+q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots$
3920.2.a.bl	$1$	$31.301$	$\Q$	None	$0$	$3$	$1$	$0$	$-$	$-$	$-$	$q+3q^{3}+q^{5}+6q^{9}+5q^{11}+3q^{13}+\cdots$
3920.2.a.bo	$2$	$31.301$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-2$	$0$	$-$	$+$	$+$	$q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(1+2\beta )q^{11}+\cdots$
3920.2.a.bp	$2$	$31.301$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-2$	$0$	$+$	$+$	$-$	$q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(2-2\beta )q^{11}+\cdots$
3920.2.a.bu	$2$	$31.301$	$\Q(\sqrt{17}) $	None	$0$	$1$	$-2$	$0$	$+$	$+$	$-$	$q+\beta q^{3}-q^{5}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
3920.2.a.bw	$2$	$31.301$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-2$	$0$	$-$	$+$	$+$	$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(3+2\beta )q^{11}+\cdots$
3920.2.a.by	$2$	$31.301$	$\Q(\sqrt{2}) $	None	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots$
3920.2.a.bz	$2$	$31.301$	$\Q(\sqrt{2}) $	None	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+(2+2\beta )q^{11}+\cdots$
3920.2.a.ca	$2$	$31.301$	$\Q(\sqrt{2}) $	None	$0$	$4$	$-2$	$0$	$-$	$+$	$+$	$q+(2+\beta )q^{3}-q^{5}+(3+4\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
3920.2.a.cb	$3$	$31.301$	3.3.1944.1	None	$0$	$0$	$-3$	$0$	$+$	$+$	$-$	$q-\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
3920.2.a.cc	$3$	$31.301$	3.3.1944.1	None	$0$	$0$	$3$	$0$	$+$	$-$	$+$	$q+\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
3920.2.a.cd	$4$	$31.301$	4.4.16448.2	None	$0$	$-2$	$4$	$0$	$+$	$-$	$+$	$q-\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$

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Elliptic curves over $\Q$
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Higher genus families
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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
3920.2.a.b	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-3\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-3q^{3}-q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots\)
3920.2.a.c	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-3\)	\(-1\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-3q^{3}-q^{5}+6q^{9}+5q^{11}+5q^{13}+\cdots\)
3920.2.a.d	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-3\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-3q^{3}+q^{5}+6q^{9}+2q^{11}+6q^{13}+\cdots\)
3920.2.a.g	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-2\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-2q^{3}+q^{5}+q^{9}-3q^{11}-5q^{13}+\cdots\)
3920.2.a.h	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-2\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-2q^{3}+q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
3920.2.a.j	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-2\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3920.2.a.k	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-2q^{9}-6q^{11}+2q^{13}+\cdots\)
3920.2.a.l	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}-2q^{9}-3q^{11}-q^{13}+\cdots\)
3920.2.a.o	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}-2q^{9}+5q^{11}+7q^{13}+\cdots\)
3920.2.a.p	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-2q^{9}+6q^{11}-4q^{13}+\cdots\)
3920.2.a.s	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{5}-3q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
3920.2.a.t	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{5}-3q^{9}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
3920.2.a.w	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}-2q^{9}-6q^{11}-2q^{13}+\cdots\)
3920.2.a.z	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}-2q^{9}+q^{11}+5q^{13}+\cdots\)
3920.2.a.ba	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}-2q^{9}+3q^{11}-5q^{13}+\cdots\)
3920.2.a.bc	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}-2q^{9}+6q^{11}+4q^{13}+\cdots\)
3920.2.a.bd	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(2\)	\(-1\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+2q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
3920.2.a.be	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(2\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+2q^{3}-q^{5}+q^{9}-3q^{11}+5q^{13}+\cdots\)
3920.2.a.bi	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(3\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+3q^{3}-q^{5}+6q^{9}+2q^{11}-6q^{13}+\cdots\)
3920.2.a.bj	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(3\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}+q^{5}+6q^{9}-q^{11}-3q^{13}+\cdots\)
3920.2.a.bk	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(3\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}+q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots\)
3920.2.a.bl	\(1\)	\(31.301\)	\(\Q\)	None	\(0\)	\(3\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+3q^{3}+q^{5}+6q^{9}+5q^{11}+3q^{13}+\cdots\)
3920.2.a.bo	\(2\)	\(31.301\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(1+2\beta )q^{11}+\cdots\)
3920.2.a.bp	\(2\)	\(31.301\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
3920.2.a.bu	\(2\)	\(31.301\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+\beta q^{3}-q^{5}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
3920.2.a.bw	\(2\)	\(31.301\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(3+2\beta )q^{11}+\cdots\)
3920.2.a.by	\(2\)	\(31.301\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
3920.2.a.bz	\(2\)	\(31.301\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+(2+2\beta )q^{11}+\cdots\)
3920.2.a.ca	\(2\)	\(31.301\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(4\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(2+\beta )q^{3}-q^{5}+(3+4\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
3920.2.a.cb	\(3\)	\(31.301\)	3.3.1944.1	None	\(0\)	\(0\)	\(-3\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
3920.2.a.cc	\(3\)	\(31.301\)	3.3.1944.1	None	\(0\)	\(0\)	\(3\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
3920.2.a.cd	\(4\)	\(31.301\)	4.4.16448.2	None	\(0\)	\(-2\)	\(4\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)

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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.