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-twists	CM/RM discriminant	Inner twist count	Is self-dual?	Analytic rank

Coefficient ring index	Coefficient ring gens.	Only for weight 1:	Projective image	Projective image type
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Results (displaying all 24 matches)

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	89	$q$-expansion
4005.2.a.a	$1$	$31.980$	$\Q$	None	$-1$	$0$	$1$	$4$	$-$	$-$	$-$	$q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-q^{10}+\cdots$
4005.2.a.b	$1$	$31.980$	$\Q$	None	$0$	$0$	$-1$	$-4$	$+$	$+$	$+$	$q-2q^{4}-q^{5}-4q^{7}-2q^{11}+4q^{13}+\cdots$
4005.2.a.c	$1$	$31.980$	$\Q$	None	$0$	$0$	$1$	$-4$	$+$	$-$	$-$	$q-2q^{4}+q^{5}-4q^{7}+2q^{11}+4q^{13}+\cdots$
4005.2.a.d	$1$	$31.980$	$\Q$	None	$1$	$0$	$-1$	$0$	$-$	$+$	$+$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-4q^{11}+\cdots$
4005.2.a.e	$2$	$31.980$	$\Q(\sqrt{2}) $	None	$-2$	$0$	$-2$	$0$	$-$	$+$	$-$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}-\beta q^{7}+\cdots$
4005.2.a.f	$2$	$31.980$	$\Q(\sqrt{3}) $	None	$0$	$0$	$-2$	$-2$	$-$	$+$	$-$	$q+\beta q^{2}+q^{4}-q^{5}+(-1+\beta )q^{7}-\beta q^{8}+\cdots$
4005.2.a.g	$2$	$31.980$	$\Q(\sqrt{17}) $	None	$1$	$0$	$-2$	$0$	$-$	$+$	$+$	$q+\beta q^{2}+(2+\beta )q^{4}-q^{5}+(4+\beta )q^{8}+\cdots$
4005.2.a.h	$2$	$31.980$	$\Q(\sqrt{5}) $	None	$2$	$0$	$2$	$2$	$-$	$-$	$-$	$q+q^{2}-q^{4}+q^{5}+(1+\beta )q^{7}-3q^{8}+\cdots$
4005.2.a.i	$3$	$31.980$	$\Q(\zeta_{18})^+$	None	$0$	$0$	$-3$	$3$	$-$	$+$	$+$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1+\beta _{2})q^{7}+\cdots$
4005.2.a.j	$3$	$31.980$	$\Q(\zeta_{14})^+$	None	$2$	$0$	$-3$	$-5$	$-$	$+$	$-$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
4005.2.a.k	$4$	$31.980$	4.4.8069.1	None	$-1$	$0$	$-4$	$12$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+3q^{7}+\cdots$
4005.2.a.l	$4$	$31.980$	4.4.725.1	None	$-1$	$0$	$4$	$2$	$-$	$-$	$-$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+\cdots$
4005.2.a.m	$4$	$31.980$	4.4.2777.1	None	$0$	$0$	$4$	$-7$	$-$	$-$	$+$	$q-\beta _{2}q^{2}+(1-\beta _{3})q^{4}+q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
4005.2.a.n	$6$	$31.980$	6.6.10407557.1	None	$4$	$0$	$6$	$1$	$-$	$-$	$-$	$q+(1+\beta _{2})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+q^{5}+\cdots$
4005.2.a.o	$7$	$31.980$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$4$	$0$	$-7$	$-16$	$-$	$+$	$+$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3})q^{4}-q^{5}+\cdots$
4005.2.a.p	$8$	$31.980$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-1$	$0$	$8$	$-6$	$-$	$-$	$+$	$q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
4005.2.a.q	$9$	$31.980$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$-5$	$0$	$9$	$-3$	$-$	$-$	$+$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4005.2.a.r	$10$	$31.980$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-6$	$0$	$-10$	$7$	$-$	$+$	$+$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4005.2.a.s	$10$	$31.980$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-1$	$0$	$-10$	$-1$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{6}q^{7}+\cdots$
4005.2.a.t	$10$	$31.980$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$0$	$10$	$9$	$-$	$-$	$-$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
4005.2.a.u	$12$	$31.980$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$-3$	$0$	$12$	$-8$	$+$	$-$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
4005.2.a.v	$12$	$31.980$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$3$	$0$	$-12$	$-8$	$+$	$+$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
4005.2.a.w	$17$	$31.980$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	$-5$	$0$	$-17$	$12$	$+$	$+$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{8}+\cdots)q^{7}+\cdots$
4005.2.a.x	$17$	$31.980$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	$5$	$0$	$17$	$12$	$+$	$-$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1+\beta _{8}+\cdots)q^{7}+\cdots$

Introduction	Features
Universe	News

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	89	$q$-expansion
4005.2.a.a	\(1\)	\(31.980\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-q^{10}+\cdots\)
4005.2.a.b	\(1\)	\(31.980\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(q-2q^{4}-q^{5}-4q^{7}-2q^{11}+4q^{13}+\cdots\)
4005.2.a.c	\(1\)	\(31.980\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(q-2q^{4}+q^{5}-4q^{7}+2q^{11}+4q^{13}+\cdots\)
4005.2.a.d	\(1\)	\(31.980\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-4q^{11}+\cdots\)
4005.2.a.e	\(2\)	\(31.980\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}-\beta q^{7}+\cdots\)
4005.2.a.f	\(2\)	\(31.980\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(0\)	\(-2\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q+\beta q^{2}+q^{4}-q^{5}+(-1+\beta )q^{7}-\beta q^{8}+\cdots\)
4005.2.a.g	\(2\)	\(31.980\)	\(\Q(\sqrt{17}) \)	None	\(1\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+\beta q^{2}+(2+\beta )q^{4}-q^{5}+(4+\beta )q^{8}+\cdots\)
4005.2.a.h	\(2\)	\(31.980\)	\(\Q(\sqrt{5}) \)	None	\(2\)	\(0\)	\(2\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}-q^{4}+q^{5}+(1+\beta )q^{7}-3q^{8}+\cdots\)
4005.2.a.i	\(3\)	\(31.980\)	\(\Q(\zeta_{18})^+\)	None	\(0\)	\(0\)	\(-3\)	\(3\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1+\beta _{2})q^{7}+\cdots\)
4005.2.a.j	\(3\)	\(31.980\)	\(\Q(\zeta_{14})^+\)	None	\(2\)	\(0\)	\(-3\)	\(-5\)	\(-\)	\(+\)	\(-\)	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
4005.2.a.k	\(4\)	\(31.980\)	4.4.8069.1	None	\(-1\)	\(0\)	\(-4\)	\(12\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+3q^{7}+\cdots\)
4005.2.a.l	\(4\)	\(31.980\)	4.4.725.1	None	\(-1\)	\(0\)	\(4\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+(-1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
4005.2.a.m	\(4\)	\(31.980\)	4.4.2777.1	None	\(0\)	\(0\)	\(4\)	\(-7\)	\(-\)	\(-\)	\(+\)	\(q-\beta _{2}q^{2}+(1-\beta _{3})q^{4}+q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
4005.2.a.n	\(6\)	\(31.980\)	6.6.10407557.1	None	\(4\)	\(0\)	\(6\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+(1+\beta _{2})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+q^{5}+\cdots\)
4005.2.a.o	\(7\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(4\)	\(0\)	\(-7\)	\(-16\)	\(-\)	\(+\)	\(+\)	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3})q^{4}-q^{5}+\cdots\)
4005.2.a.p	\(8\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-1\)	\(0\)	\(8\)	\(-6\)	\(-\)	\(-\)	\(+\)	\(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
4005.2.a.q	\(9\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(-5\)	\(0\)	\(9\)	\(-3\)	\(-\)	\(-\)	\(+\)	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4005.2.a.r	\(10\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-6\)	\(0\)	\(-10\)	\(7\)	\(-\)	\(+\)	\(+\)	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4005.2.a.s	\(10\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-1\)	\(0\)	\(-10\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{6}q^{7}+\cdots\)
4005.2.a.t	\(10\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(0\)	\(10\)	\(9\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
4005.2.a.u	\(12\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(-3\)	\(0\)	\(12\)	\(-8\)	\(+\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
4005.2.a.v	\(12\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(3\)	\(0\)	\(-12\)	\(-8\)	\(+\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
4005.2.a.w	\(17\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	\(-5\)	\(0\)	\(-17\)	\(12\)	\(+\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{8}+\cdots)q^{7}+\cdots\)
4005.2.a.x	\(17\)	\(31.980\)	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	\(5\)	\(0\)	\(17\)	\(12\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1+\beta _{8}+\cdots)q^{7}+\cdots\)

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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.