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 (displaying all 30 matches)

Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
7524.2.a.a	$1$	$60.079$	$\Q$	None	$0$	$0$	$-2$	$-4$	$+$	$q-2q^{5}-4q^{7}-q^{11}+q^{13}+3q^{17}+\cdots$
7524.2.a.b	$1$	$60.079$	$\Q$	None	$0$	$0$	$-2$	$0$	$-$	$q-2q^{5}-q^{11}+4q^{13}+2q^{17}+q^{19}+\cdots$
7524.2.a.c	$1$	$60.079$	$\Q$	None	$0$	$0$	$-1$	$0$	$+$	$q-q^{5}+q^{11}-2q^{13}+4q^{17}+q^{19}+\cdots$
7524.2.a.d	$1$	$60.079$	$\Q$	None	$0$	$0$	$0$	$0$	$-$	$q-q^{11}+2q^{13}+4q^{17}-q^{19}-4q^{23}+\cdots$
7524.2.a.e	$1$	$60.079$	$\Q$	None	$0$	$0$	$0$	$0$	$+$	$q+q^{11}+2q^{13}-4q^{17}-q^{19}+4q^{23}+\cdots$
7524.2.a.f	$1$	$60.079$	$\Q$	None	$0$	$0$	$0$	$2$	$+$	$q+2q^{7}+q^{11}+5q^{13}-3q^{17}+q^{19}+\cdots$
7524.2.a.g	$1$	$60.079$	$\Q$	None	$0$	$0$	$2$	$-4$	$-$	$q+2q^{5}-4q^{7}+q^{11}+q^{13}-3q^{17}+\cdots$
7524.2.a.h	$2$	$60.079$	$\Q(\sqrt{2}) $	None	$0$	$0$	$2$	$0$	$+$	$q+q^{5}+\beta q^{7}-q^{11}-\beta q^{13}-\beta q^{17}+\cdots$
7524.2.a.i	$3$	$60.079$	3.3.321.1	None	$0$	$0$	$-1$	$-5$	$+$	$q+\beta _{2}q^{5}+(-2+\beta _{1})q^{7}+q^{11}+(1+\cdots)q^{13}+\cdots$
7524.2.a.j	$3$	$60.079$	3.3.993.1	None	$0$	$0$	$-1$	$-1$	$+$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}-q^{11}+(-1-\beta _{1}+\cdots)q^{13}+\cdots$
7524.2.a.k	$3$	$60.079$	3.3.785.1	None	$0$	$0$	$-1$	$-1$	$+$	$q-\beta _{2}q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+q^{11}+\cdots$
7524.2.a.l	$3$	$60.079$	$\Q(\zeta_{14})^+$	None	$0$	$0$	$3$	$-3$	$-$	$q+(1+\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$
7524.2.a.m	$3$	$60.079$	$\Q(\zeta_{18})^+$	None	$0$	$0$	$3$	$-3$	$-$	$q+(1+\beta _{1})q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots$
7524.2.a.n	$4$	$60.079$	4.4.171777.1	None	$0$	$0$	$-1$	$5$	$+$	$q-\beta _{3}q^{5}+(1+\beta _{1})q^{7}-q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
7524.2.a.o	$4$	$60.079$	4.4.23665.1	None	$0$	$0$	$3$	$3$	$-$	$q+(1-\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots$
7524.2.a.p	$4$	$60.079$	4.4.161473.1	None	$0$	$0$	$3$	$3$	$-$	$q+(1-\beta _{1})q^{5}+(1+\beta _{3})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots$
7524.2.a.q	$6$	$60.079$	6.6.744786576.1	None	$0$	$0$	$-5$	$-2$	$-$	$q+(-1-\beta _{5})q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
7524.2.a.r	$6$	$60.079$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$0$	$0$	$0$	$2$	$-$	$q+\beta _{5}q^{5}+\beta _{4}q^{7}-q^{11}+\beta _{3}q^{13}+\cdots$
7524.2.a.s	$7$	$60.079$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$0$	$-4$	$-2$	$+$	$q+(-1+\beta _{3})q^{5}-\beta _{6}q^{7}+q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
7524.2.a.t	$7$	$60.079$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$0$	$-2$	$6$	$+$	$q+\beta _{5}q^{5}+(1-\beta _{1})q^{7}-q^{11}+\beta _{6}q^{13}+\cdots$
7524.2.a.u	$7$	$60.079$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$0$	$2$	$6$	$-$	$q-\beta _{5}q^{5}+(1-\beta _{1})q^{7}+q^{11}+\beta _{6}q^{13}+\cdots$
7524.2.a.v	$7$	$60.079$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$0$	$4$	$-2$	$-$	$q+(1-\beta _{3})q^{5}-\beta _{6}q^{7}-q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
7524.2.c.a	$72$	$60.079$		None	$0$	$0$	$0$	$0$
7524.2.f.a	$64$	$60.079$		None	$0$	$0$	$0$	$0$
7524.2.l.a	$4$	$60.079$	$\Q(\sqrt{-3}, \sqrt{-19})$	$\Q(\sqrt{-19}) $	$0$	$0$	$2$	$0$		$q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots$
7524.2.l.b	$8$	$60.079$	8.0.$\cdots$.6	$\Q(\sqrt{-627}) $	$0$	$0$	$0$	$0$		$q-\beta _{6}q^{11}-\beta _{1}q^{13}+\beta _{3}q^{17}-\beta _{4}q^{19}+\cdots$
7524.2.l.c	$8$	$60.079$	8.0.2702336256.1	$\Q(\sqrt{-19}) $	$0$	$0$	$0$	$0$		$q+(\beta _{5}+\beta _{7})q^{5}+(\beta _{3}-\beta _{4})q^{7}+(\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots$
7524.2.l.d	$16$	$60.079$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$-4$	$0$		$q+\beta _{2}q^{5}+(\beta _{9}-\beta _{12})q^{7}+(-\beta _{3}-\beta _{9}+\cdots)q^{11}+\cdots$
7524.2.l.e	$24$	$60.079$		None	$0$	$0$	$0$	$0$
7524.2.l.f	$40$	$60.079$		None	$0$	$0$	$4$	$0$

Introduction	Features
Universe	News

Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
7524.2.a.a	\(1\)	\(60.079\)	\(\Q\)	None	\(0\)	\(0\)	\(-2\)	\(-4\)	\(+\)	\(q-2q^{5}-4q^{7}-q^{11}+q^{13}+3q^{17}+\cdots\)
7524.2.a.b	\(1\)	\(60.079\)	\(\Q\)	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(q-2q^{5}-q^{11}+4q^{13}+2q^{17}+q^{19}+\cdots\)
7524.2.a.c	\(1\)	\(60.079\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(0\)	\(+\)	\(q-q^{5}+q^{11}-2q^{13}+4q^{17}+q^{19}+\cdots\)
7524.2.a.d	\(1\)	\(60.079\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q-q^{11}+2q^{13}+4q^{17}-q^{19}-4q^{23}+\cdots\)
7524.2.a.e	\(1\)	\(60.079\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q+q^{11}+2q^{13}-4q^{17}-q^{19}+4q^{23}+\cdots\)
7524.2.a.f	\(1\)	\(60.079\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(2\)	\(+\)	\(q+2q^{7}+q^{11}+5q^{13}-3q^{17}+q^{19}+\cdots\)
7524.2.a.g	\(1\)	\(60.079\)	\(\Q\)	None	\(0\)	\(0\)	\(2\)	\(-4\)	\(-\)	\(q+2q^{5}-4q^{7}+q^{11}+q^{13}-3q^{17}+\cdots\)
7524.2.a.h	\(2\)	\(60.079\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	\(+\)	\(q+q^{5}+\beta q^{7}-q^{11}-\beta q^{13}-\beta q^{17}+\cdots\)
7524.2.a.i	\(3\)	\(60.079\)	3.3.321.1	None	\(0\)	\(0\)	\(-1\)	\(-5\)	\(+\)	\(q+\beta _{2}q^{5}+(-2+\beta _{1})q^{7}+q^{11}+(1+\cdots)q^{13}+\cdots\)
7524.2.a.j	\(3\)	\(60.079\)	3.3.993.1	None	\(0\)	\(0\)	\(-1\)	\(-1\)	\(+\)	\(q-\beta _{1}q^{5}-\beta _{2}q^{7}-q^{11}+(-1-\beta _{1}+\cdots)q^{13}+\cdots\)
7524.2.a.k	\(3\)	\(60.079\)	3.3.785.1	None	\(0\)	\(0\)	\(-1\)	\(-1\)	\(+\)	\(q-\beta _{2}q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+q^{11}+\cdots\)
7524.2.a.l	\(3\)	\(60.079\)	\(\Q(\zeta_{14})^+\)	None	\(0\)	\(0\)	\(3\)	\(-3\)	\(-\)	\(q+(1+\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
7524.2.a.m	\(3\)	\(60.079\)	\(\Q(\zeta_{18})^+\)	None	\(0\)	\(0\)	\(3\)	\(-3\)	\(-\)	\(q+(1+\beta _{1})q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
7524.2.a.n	\(4\)	\(60.079\)	4.4.171777.1	None	\(0\)	\(0\)	\(-1\)	\(5\)	\(+\)	\(q-\beta _{3}q^{5}+(1+\beta _{1})q^{7}-q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
7524.2.a.o	\(4\)	\(60.079\)	4.4.23665.1	None	\(0\)	\(0\)	\(3\)	\(3\)	\(-\)	\(q+(1-\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots\)
7524.2.a.p	\(4\)	\(60.079\)	4.4.161473.1	None	\(0\)	\(0\)	\(3\)	\(3\)	\(-\)	\(q+(1-\beta _{1})q^{5}+(1+\beta _{3})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
7524.2.a.q	\(6\)	\(60.079\)	6.6.744786576.1	None	\(0\)	\(0\)	\(-5\)	\(-2\)	\(-\)	\(q+(-1-\beta _{5})q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
7524.2.a.r	\(6\)	\(60.079\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(2\)	\(-\)	\(q+\beta _{5}q^{5}+\beta _{4}q^{7}-q^{11}+\beta _{3}q^{13}+\cdots\)
7524.2.a.s	\(7\)	\(60.079\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(0\)	\(-4\)	\(-2\)	\(+\)	\(q+(-1+\beta _{3})q^{5}-\beta _{6}q^{7}+q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
7524.2.a.t	\(7\)	\(60.079\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(0\)	\(-2\)	\(6\)	\(+\)	\(q+\beta _{5}q^{5}+(1-\beta _{1})q^{7}-q^{11}+\beta _{6}q^{13}+\cdots\)
7524.2.a.u	\(7\)	\(60.079\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(0\)	\(2\)	\(6\)	\(-\)	\(q-\beta _{5}q^{5}+(1-\beta _{1})q^{7}+q^{11}+\beta _{6}q^{13}+\cdots\)
7524.2.a.v	\(7\)	\(60.079\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(0\)	\(4\)	\(-2\)	\(-\)	\(q+(1-\beta _{3})q^{5}-\beta _{6}q^{7}-q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
7524.2.c.a	\(72\)	\(60.079\)		None	\(0\)	\(0\)	\(0\)	\(0\)
7524.2.f.a	\(64\)	\(60.079\)		None	\(0\)	\(0\)	\(0\)	\(0\)
7524.2.l.a	\(4\)	\(60.079\)	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)	\(0\)	\(0\)	\(2\)	\(0\)		\(q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
7524.2.l.b	\(8\)	\(60.079\)	8.0.\(\cdots\).6	\(\Q(\sqrt{-627}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{6}q^{11}-\beta _{1}q^{13}+\beta _{3}q^{17}-\beta _{4}q^{19}+\cdots\)
7524.2.l.c	\(8\)	\(60.079\)	8.0.2702336256.1	\(\Q(\sqrt{-19}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{5}+\beta _{7})q^{5}+(\beta _{3}-\beta _{4})q^{7}+(\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)
7524.2.l.d	\(16\)	\(60.079\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+\beta _{2}q^{5}+(\beta _{9}-\beta _{12})q^{7}+(-\beta _{3}-\beta _{9}+\cdots)q^{11}+\cdots\)
7524.2.l.e	\(24\)	\(60.079\)		None	\(0\)	\(0\)	\(0\)	\(0\)
7524.2.l.f	\(40\)	\(60.079\)		None	\(0\)	\(0\)	\(4\)	\(0\)

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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.