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 (21 matches)

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Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
2672.1.g.a	$5$	$1.334$	$\Q(\zeta_{22})^+$	$\Q(\sqrt{-167}) $	None	$0$	$1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}-\beta _{2}q^{7}+\cdots$
2672.1.i.a	$2$	$1.334$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-167}) $	None	$0$	$-2$	$0$	$0$		$q+iq^{2}+(-1+i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
2672.1.i.b	$20$	$1.334$	$\Q(\zeta_{44})$	$\Q(\sqrt{-167}) $	None	$0$	$2$	$0$	$0$		$q-\zeta_{44}^{7}q^{2}+(\zeta_{44}^{5}+\zeta_{44}^{6})q^{3}+\zeta_{44}^{14}q^{4}+\cdots$
2672.2.a.a	$1$	$21.336$	$\Q$	None	None	$0$	$0$	$3$	$-1$	$+$	$q+3q^{5}-q^{7}-3q^{9}-2q^{13}-2q^{17}+\cdots$
2672.2.a.b	$2$	$21.336$	$\Q(\sqrt{5}) $	None	None	$0$	$-3$	$0$	$7$	$-$	$q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+(4-\beta )q^{7}+\cdots$
2672.2.a.c	$2$	$21.336$	$\Q(\sqrt{13}) $	None	None	$0$	$-1$	$-6$	$-3$	$+$	$q-\beta q^{3}-3q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots$
2672.2.a.d	$2$	$21.336$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$2$	$6$	$-$	$q+2\beta q^{3}+(1+\beta )q^{5}+3q^{7}+5q^{9}+\cdots$
2672.2.a.e	$2$	$21.336$	$\Q(\sqrt{5}) $	None	None	$0$	$1$	$-2$	$0$	$+$	$q+\beta q^{3}-q^{5}+(1-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2672.2.a.f	$2$	$21.336$	$\Q(\sqrt{5}) $	None	None	$0$	$1$	$-2$	$5$	$+$	$q+\beta q^{3}-q^{5}+(3-\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2672.2.a.g	$2$	$21.336$	$\Q(\sqrt{5}) $	None	None	$0$	$3$	$-4$	$6$	$-$	$q+(1+\beta )q^{3}+(-3+2\beta )q^{5}+3q^{7}+\cdots$
2672.2.a.h	$3$	$21.336$	3.3.733.1	None	None	$0$	$-1$	$-3$	$-3$	$+$	$q-\beta _{1}q^{3}-q^{5}-q^{7}+(2+\beta _{2})q^{9}+(-3+\cdots)q^{11}+\cdots$
2672.2.a.i	$3$	$21.336$	3.3.469.1	None	None	$0$	$1$	$0$	$0$	$-$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
2672.2.a.j	$5$	$21.336$	5.5.826865.1	None	None	$0$	$-3$	$10$	$-9$	$+$	$q+(-1+\beta _{2})q^{3}+2q^{5}+(-2+\beta _{3}+\cdots)q^{7}+\cdots$
2672.2.a.k	$7$	$21.336$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	None	$0$	$4$	$-2$	$12$	$-$	$q+(1+\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots$
2672.2.a.l	$7$	$21.336$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	None	$0$	$6$	$0$	$1$	$-$	$q+(1-\beta _{1})q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
2672.2.a.m	$9$	$21.336$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	None	$0$	$1$	$-8$	$-2$	$+$	$q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{8})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
2672.2.a.n	$12$	$21.336$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$-5$	$-2$	$-10$	$+$	$q-\beta _{1}q^{3}+\beta _{9}q^{5}+(-1-\beta _{11})q^{7}+\cdots$
2672.2.a.o	$12$	$21.336$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$-3$	$4$	$-11$	$-$	$q-\beta _{5}q^{3}-\beta _{8}q^{5}+(-1+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots$
2672.2.a.p	$12$	$21.336$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$1$	$8$	$4$	$-$	$q+\beta _{1}q^{3}+(1-\beta _{9})q^{5}-\beta _{11}q^{7}+(2+\cdots)q^{9}+\cdots$
2672.2.b.a	$28$	$21.336$		None	None	$0$	$0$	$0$	$0$
2672.2.b.b	$56$	$21.336$		None	None	$0$	$0$	$0$	$0$

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Label	Dim.	\(A\)	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
2672.1.g.a	\(5\)	\(1.334\)	\(\Q(\zeta_{22})^+\)	\(\Q(\sqrt{-167}) \)	None	\(0\)	\(1\)	\(0\)	\(1\)		\(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}-\beta _{2}q^{7}+\cdots\)
2672.1.i.a	\(2\)	\(1.334\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-167}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)		\(q+iq^{2}+(-1+i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots\)
2672.1.i.b	\(20\)	\(1.334\)	\(\Q(\zeta_{44})\)	\(\Q(\sqrt{-167}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)		\(q-\zeta_{44}^{7}q^{2}+(\zeta_{44}^{5}+\zeta_{44}^{6})q^{3}+\zeta_{44}^{14}q^{4}+\cdots\)
2672.2.a.a	\(1\)	\(21.336\)	\(\Q\)	None	None	\(0\)	\(0\)	\(3\)	\(-1\)	\(+\)	\(q+3q^{5}-q^{7}-3q^{9}-2q^{13}-2q^{17}+\cdots\)
2672.2.a.b	\(2\)	\(21.336\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(-3\)	\(0\)	\(7\)	\(-\)	\(q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+(4-\beta )q^{7}+\cdots\)
2672.2.a.c	\(2\)	\(21.336\)	\(\Q(\sqrt{13}) \)	None	None	\(0\)	\(-1\)	\(-6\)	\(-3\)	\(+\)	\(q-\beta q^{3}-3q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
2672.2.a.d	\(2\)	\(21.336\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(2\)	\(6\)	\(-\)	\(q+2\beta q^{3}+(1+\beta )q^{5}+3q^{7}+5q^{9}+\cdots\)
2672.2.a.e	\(2\)	\(21.336\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(+\)	\(q+\beta q^{3}-q^{5}+(1-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2672.2.a.f	\(2\)	\(21.336\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(1\)	\(-2\)	\(5\)	\(+\)	\(q+\beta q^{3}-q^{5}+(3-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2672.2.a.g	\(2\)	\(21.336\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(3\)	\(-4\)	\(6\)	\(-\)	\(q+(1+\beta )q^{3}+(-3+2\beta )q^{5}+3q^{7}+\cdots\)
2672.2.a.h	\(3\)	\(21.336\)	3.3.733.1	None	None	\(0\)	\(-1\)	\(-3\)	\(-3\)	\(+\)	\(q-\beta _{1}q^{3}-q^{5}-q^{7}+(2+\beta _{2})q^{9}+(-3+\cdots)q^{11}+\cdots\)
2672.2.a.i	\(3\)	\(21.336\)	3.3.469.1	None	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
2672.2.a.j	\(5\)	\(21.336\)	5.5.826865.1	None	None	\(0\)	\(-3\)	\(10\)	\(-9\)	\(+\)	\(q+(-1+\beta _{2})q^{3}+2q^{5}+(-2+\beta _{3}+\cdots)q^{7}+\cdots\)
2672.2.a.k	\(7\)	\(21.336\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	None	\(0\)	\(4\)	\(-2\)	\(12\)	\(-\)	\(q+(1+\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots\)
2672.2.a.l	\(7\)	\(21.336\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	None	\(0\)	\(6\)	\(0\)	\(1\)	\(-\)	\(q+(1-\beta _{1})q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2672.2.a.m	\(9\)	\(21.336\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	None	\(0\)	\(1\)	\(-8\)	\(-2\)	\(+\)	\(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{8})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2672.2.a.n	\(12\)	\(21.336\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(-5\)	\(-2\)	\(-10\)	\(+\)	\(q-\beta _{1}q^{3}+\beta _{9}q^{5}+(-1-\beta _{11})q^{7}+\cdots\)
2672.2.a.o	\(12\)	\(21.336\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(-3\)	\(4\)	\(-11\)	\(-\)	\(q-\beta _{5}q^{3}-\beta _{8}q^{5}+(-1+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots\)
2672.2.a.p	\(12\)	\(21.336\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(1\)	\(8\)	\(4\)	\(-\)	\(q+\beta _{1}q^{3}+(1-\beta _{9})q^{5}-\beta _{11}q^{7}+(2+\cdots)q^{9}+\cdots\)
2672.2.b.a	\(28\)	\(21.336\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
2672.2.b.b	\(56\)	\(21.336\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)

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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.