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 (27 matches)

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Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	3	5	7	$q$-expansion
3675.2.a.b	$1$	$29.345$	$\Q$	None	$-2$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}+2q^{11}+\cdots$
3675.2.a.j	$1$	$29.345$	$\Q$	None	$1$	$-1$	$0$	$0$	$+$	$+$	$-$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
3675.2.a.l	$1$	$29.345$	$\Q$	None	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
3675.2.a.q	$1$	$29.345$	$\Q$	None	$2$	$1$	$0$	$0$	$-$	$-$	$-$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{9}+2q^{11}+\cdots$
3675.2.a.r	$2$	$29.345$	$\Q(\sqrt{5}) $	None	$-3$	$2$	$0$	$0$	$-$	$-$	$-$	$q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots$
3675.2.a.s	$2$	$29.345$	$\Q(\sqrt{2}) $	None	$-2$	$-2$	$0$	$0$	$+$	$+$	$-$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots$
3675.2.a.v	$2$	$29.345$	$\Q(\sqrt{5}) $	None	$-1$	$2$	$0$	$0$	$-$	$-$	$-$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
3675.2.a.x	$2$	$29.345$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$q+\beta q^{2}-q^{3}-\beta q^{6}-2\beta q^{8}+q^{9}+\cdots$
3675.2.a.y	$2$	$29.345$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-\beta q^{8}+\cdots$
3675.2.a.z	$2$	$29.345$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$q+\beta q^{2}+q^{3}+\beta q^{6}-2\beta q^{8}+q^{9}+\cdots$
3675.2.a.ba	$2$	$29.345$	$\Q(\sqrt{5}) $	None	$1$	$-2$	$0$	$0$	$+$	$+$	$-$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
3675.2.a.be	$2$	$29.345$	$\Q(\sqrt{3}) $	None	$2$	$-2$	$0$	$0$	$+$	$+$	$-$	$q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
3675.2.a.bf	$2$	$29.345$	$\Q(\sqrt{2}) $	None	$2$	$2$	$0$	$0$	$-$	$+$	$+$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots$
3675.2.a.bg	$2$	$29.345$	$\Q(\sqrt{3}) $	None	$2$	$2$	$0$	$0$	$-$	$+$	$+$	$q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+(1+\beta )q^{6}+\cdots$
3675.2.a.bh	$2$	$29.345$	$\Q(\sqrt{5}) $	None	$3$	$-2$	$0$	$0$	$+$	$+$	$-$	$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots$
3675.2.a.bj	$3$	$29.345$	3.3.148.1	None	$1$	$3$	$0$	$0$	$-$	$-$	$-$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3675.2.a.bl	$4$	$29.345$	4.4.4352.1	None	$-4$	$4$	$0$	$0$	$-$	$+$	$+$	$q+(-1-\beta _{1}+\beta _{3})q^{2}+q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$
3675.2.a.bm	$4$	$29.345$	4.4.2624.1	None	$-2$	$-4$	$0$	$0$	$+$	$-$	$+$	$q+(-1+\beta _{1})q^{2}-q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
3675.2.a.bq	$4$	$29.345$	4.4.88404.1	None	$-1$	$-4$	$0$	$0$	$+$	$+$	$-$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3675.2.a.br	$4$	$29.345$	4.4.88404.1	None	$-1$	$4$	$0$	$0$	$-$	$+$	$+$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
3675.2.a.bs	$4$	$29.345$	$\Q(\zeta_{24})^+$	None	$0$	$-4$	$0$	$0$	$+$	$-$	$+$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-\beta _{1}q^{6}+\beta _{3}q^{8}+\cdots$
3675.2.a.bv	$4$	$29.345$	4.4.4400.1	None	$0$	$4$	$0$	$0$	$-$	$-$	$-$	$q-\beta _{2}q^{2}+q^{3}+(2-\beta _{3})q^{4}-\beta _{2}q^{6}+\cdots$
3675.2.a.bw	$4$	$29.345$	4.4.88404.1	None	$1$	$-4$	$0$	$0$	$+$	$-$	$+$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
3675.2.a.bx	$4$	$29.345$	4.4.88404.1	None	$1$	$4$	$0$	$0$	$-$	$-$	$-$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3675.2.a.bz	$4$	$29.345$	4.4.11344.1	None	$2$	$-4$	$0$	$0$	$+$	$-$	$+$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
3675.2.a.ca	$4$	$29.345$	4.4.2624.1	None	$2$	$4$	$0$	$0$	$-$	$+$	$+$	$q+(1-\beta _{1})q^{2}+q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
3675.2.a.cb	$4$	$29.345$	4.4.11344.1	None	$2$	$4$	$0$	$0$	$-$	$-$	$-$	$q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$

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Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	3	5	7	$q$-expansion
3675.2.a.b	\(1\)	\(29.345\)	\(\Q\)	None	\(-2\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}+2q^{11}+\cdots\)
3675.2.a.j	\(1\)	\(29.345\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
3675.2.a.l	\(1\)	\(29.345\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
3675.2.a.q	\(1\)	\(29.345\)	\(\Q\)	None	\(2\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{9}+2q^{11}+\cdots\)
3675.2.a.r	\(2\)	\(29.345\)	\(\Q(\sqrt{5}) \)	None	\(-3\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots\)
3675.2.a.s	\(2\)	\(29.345\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
3675.2.a.v	\(2\)	\(29.345\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
3675.2.a.x	\(2\)	\(29.345\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+\beta q^{2}-q^{3}-\beta q^{6}-2\beta q^{8}+q^{9}+\cdots\)
3675.2.a.y	\(2\)	\(29.345\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-\beta q^{8}+\cdots\)
3675.2.a.z	\(2\)	\(29.345\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+\beta q^{2}+q^{3}+\beta q^{6}-2\beta q^{8}+q^{9}+\cdots\)
3675.2.a.ba	\(2\)	\(29.345\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
3675.2.a.be	\(2\)	\(29.345\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
3675.2.a.bf	\(2\)	\(29.345\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
3675.2.a.bg	\(2\)	\(29.345\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
3675.2.a.bh	\(2\)	\(29.345\)	\(\Q(\sqrt{5}) \)	None	\(3\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots\)
3675.2.a.bj	\(3\)	\(29.345\)	3.3.148.1	None	\(1\)	\(3\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
3675.2.a.bl	\(4\)	\(29.345\)	4.4.4352.1	None	\(-4\)	\(4\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(-1-\beta _{1}+\beta _{3})q^{2}+q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
3675.2.a.bm	\(4\)	\(29.345\)	4.4.2624.1	None	\(-2\)	\(-4\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+(-1+\beta _{1})q^{2}-q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
3675.2.a.bq	\(4\)	\(29.345\)	4.4.88404.1	None	\(-1\)	\(-4\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
3675.2.a.br	\(4\)	\(29.345\)	4.4.88404.1	None	\(-1\)	\(4\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
3675.2.a.bs	\(4\)	\(29.345\)	\(\Q(\zeta_{24})^+\)	None	\(0\)	\(-4\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-\beta _{1}q^{6}+\beta _{3}q^{8}+\cdots\)
3675.2.a.bv	\(4\)	\(29.345\)	4.4.4400.1	None	\(0\)	\(4\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{2}q^{2}+q^{3}+(2-\beta _{3})q^{4}-\beta _{2}q^{6}+\cdots\)
3675.2.a.bw	\(4\)	\(29.345\)	4.4.88404.1	None	\(1\)	\(-4\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
3675.2.a.bx	\(4\)	\(29.345\)	4.4.88404.1	None	\(1\)	\(4\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
3675.2.a.bz	\(4\)	\(29.345\)	4.4.11344.1	None	\(2\)	\(-4\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
3675.2.a.ca	\(4\)	\(29.345\)	4.4.2624.1	None	\(2\)	\(4\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(1-\beta _{1})q^{2}+q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
3675.2.a.cb	\(4\)	\(29.345\)	4.4.11344.1	None	\(2\)	\(4\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)

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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.