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 (1-50 of 87 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
555.1.b.a	$8$	$0.277$	$\Q(\zeta_{16})$	$\Q(\sqrt{-111}) $	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+\zeta_{16}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
555.2.a.a	$1$	$4.432$	$\Q$	None	None	$0$	$1$	$-1$	$-2$	$-$	$q+q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots$
555.2.a.b	$1$	$4.432$	$\Q$	None	None	$0$	$1$	$1$	$2$	$-$	$q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-2q^{12}+\cdots$
555.2.a.c	$2$	$4.432$	$\Q(\sqrt{5}) $	None	None	$-3$	$2$	$2$	$-4$	$+$	$q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+q^{5}+\cdots$
555.2.a.d	$2$	$4.432$	$\Q(\sqrt{13}) $	None	None	$-1$	$-2$	$2$	$-6$	$+$	$q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
555.2.a.e	$2$	$4.432$	$\Q(\sqrt{5}) $	None	None	$-1$	$2$	$-2$	$-2$	$+$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
555.2.a.f	$2$	$4.432$	$\Q(\sqrt{5}) $	None	None	$1$	$-2$	$-2$	$0$	$+$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
555.2.a.g	$2$	$4.432$	$\Q(\sqrt{13}) $	None	None	$1$	$2$	$-2$	$2$	$-$	$q+\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots$
555.2.a.h	$3$	$4.432$	3.3.469.1	None	None	$1$	$-3$	$3$	$4$	$-$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
555.2.a.i	$3$	$4.432$	3.3.229.1	None	None	$2$	$3$	$3$	$-4$	$-$	$q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+q^{5}+\cdots$
555.2.a.j	$5$	$4.432$	5.5.600268.1	None	None	$-3$	$-5$	$-5$	$2$	$-$	$q+(-1+\beta _{3})q^{2}-q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots$
555.2.c.a	$2$	$4.432$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-2$	$0$		$q+2iq^{2}+iq^{3}-2q^{4}+(-1+2i)q^{5}+\cdots$
555.2.c.b	$8$	$4.432$	8.0.309760000.3	None	None	$0$	$0$	$0$	$0$		$q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
555.2.c.c	$26$	$4.432$		None	None	$0$	$0$	$-2$	$0$
555.2.e.a	$2$	$4.432$	$\Q(\sqrt{-1}) $	None	None	$0$	$-2$	$0$	$-8$		$q-q^{3}+2q^{4}+iq^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$
555.2.e.b	$10$	$4.432$	10.0.$\cdots$.1	None	None	$0$	$10$	$0$	$16$		$q+\beta _{3}q^{2}+q^{3}+(-1+\beta _{1})q^{4}+\beta _{6}q^{5}+\cdots$
555.2.e.c	$12$	$4.432$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$-12$	$0$	$8$		$q-\beta _{8}q^{2}-q^{3}+(-2-\beta _{7})q^{4}+\beta _{2}q^{5}+\cdots$
555.2.g.a	$40$	$4.432$		None	None	$0$	$0$	$0$	$0$
555.2.i.a	$2$	$4.432$	$\Q(\sqrt{-3}) $	None	None	$-1$	$-1$	$1$	$-1$		$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
555.2.i.b	$4$	$4.432$	$\Q(\sqrt{2}, \sqrt{-3})$	None	None	$-2$	$-2$	$2$	$2$		$q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
555.2.i.c	$4$	$4.432$	$\Q(\zeta_{12})$	None	None	$0$	$-2$	$2$	$-2$		$q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{3}+(-1+\cdots)q^{4}+\cdots$
555.2.i.d	$10$	$4.432$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	None	$1$	$-5$	$-5$	$-1$		$q+(-\beta _{1}+\beta _{2})q^{2}-\beta _{6}q^{3}+(\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots$
555.2.i.e	$14$	$4.432$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	None	$-1$	$7$	$-7$	$5$		$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{4}+\beta _{5}+\beta _{7})q^{4}+\cdots$
555.2.i.f	$14$	$4.432$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	None	$-1$	$7$	$7$	$1$		$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{3}-\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots$
555.2.j.a	$76$	$4.432$		None	None	$0$	$0$	$4$	$0$
555.2.m.a	$16$	$4.432$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+(\beta _{3}-\beta _{10})q^{3}-2\beta _{9}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
555.2.m.b	$128$	$4.432$		None	None	$0$	$0$	$0$	$0$
555.2.n.a	$32$	$4.432$		$\Q(\sqrt{-111}) $	None	$0$	$0$	$0$	$0$
555.2.n.b	$112$	$4.432$		None	None	$0$	$-8$	$0$	$-8$
555.2.o.a	$144$	$4.432$		None	None	$0$	$0$	$0$	$-8$
555.2.s.a	$104$	$4.432$		None	None	$0$	$0$	$0$	$0$
555.2.t.a	$76$	$4.432$		None	None	$-4$	$0$	$-8$	$0$
555.2.x.a	$80$	$4.432$		None	None	$0$	$0$	$-12$	$0$
555.2.z.a	$20$	$4.432$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$6$	$-10$	$0$	$2$		$q-\beta _{4}q^{2}+(-1-\beta _{2})q^{3}+(\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots$
555.2.z.b	$28$	$4.432$		None	None	$6$	$14$	$0$	$-6$
555.2.bb.a	$72$	$4.432$		None	None	$0$	$0$	$-2$	$0$
555.2.bc.a	$6$	$4.432$	$\Q(\zeta_{18})$	None	None	$0$	$0$	$0$	$3$		$q-\zeta_{18}^{2}q^{3}+2\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
555.2.bc.b	$36$	$4.432$		None	None	$3$	$0$	$0$	$12$
555.2.bc.c	$36$	$4.432$		None	None	$3$	$0$	$0$	$-6$
555.2.bc.d	$36$	$4.432$		None	None	$3$	$0$	$0$	$0$
555.2.bc.e	$42$	$4.432$		None	None	$3$	$0$	$0$	$-3$
555.2.bd.a	$152$	$4.432$		None	None	$4$	$0$	$8$	$0$
555.2.bg.a	$208$	$4.432$		None	None	$0$	$0$	$0$	$0$
555.2.bh.a	$288$	$4.432$		None	None	$0$	$-4$	$0$	$-4$
555.2.bi.a	$288$	$4.432$		None	None	$0$	$0$	$0$	$-4$
555.2.bm.a	$288$	$4.432$		None	None	$0$	$0$	$0$	$0$
555.2.bn.a	$152$	$4.432$		None	None	$0$	$0$	$-4$	$0$
555.2.bp.a	$240$	$4.432$		None	None	$0$	$0$	$12$	$0$
555.2.bs.a	$216$	$4.432$		None	None	$0$	$0$	$6$	$0$
555.2.bt.a	$72$	$4.432$		None	None	$-6$	$0$	$0$	$-12$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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
555.1.b.a	\(8\)	\(0.277\)	\(\Q(\zeta_{16})\)	\(\Q(\sqrt{-111}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+\zeta_{16}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
555.2.a.a	\(1\)	\(4.432\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-1\)	\(-2\)	\(-\)	\(q+q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
555.2.a.b	\(1\)	\(4.432\)	\(\Q\)	None	None	\(0\)	\(1\)	\(1\)	\(2\)	\(-\)	\(q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-2q^{12}+\cdots\)
555.2.a.c	\(2\)	\(4.432\)	\(\Q(\sqrt{5}) \)	None	None	\(-3\)	\(2\)	\(2\)	\(-4\)	\(+\)	\(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+q^{5}+\cdots\)
555.2.a.d	\(2\)	\(4.432\)	\(\Q(\sqrt{13}) \)	None	None	\(-1\)	\(-2\)	\(2\)	\(-6\)	\(+\)	\(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
555.2.a.e	\(2\)	\(4.432\)	\(\Q(\sqrt{5}) \)	None	None	\(-1\)	\(2\)	\(-2\)	\(-2\)	\(+\)	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
555.2.a.f	\(2\)	\(4.432\)	\(\Q(\sqrt{5}) \)	None	None	\(1\)	\(-2\)	\(-2\)	\(0\)	\(+\)	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
555.2.a.g	\(2\)	\(4.432\)	\(\Q(\sqrt{13}) \)	None	None	\(1\)	\(2\)	\(-2\)	\(2\)	\(-\)	\(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
555.2.a.h	\(3\)	\(4.432\)	3.3.469.1	None	None	\(1\)	\(-3\)	\(3\)	\(4\)	\(-\)	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
555.2.a.i	\(3\)	\(4.432\)	3.3.229.1	None	None	\(2\)	\(3\)	\(3\)	\(-4\)	\(-\)	\(q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+q^{5}+\cdots\)
555.2.a.j	\(5\)	\(4.432\)	5.5.600268.1	None	None	\(-3\)	\(-5\)	\(-5\)	\(2\)	\(-\)	\(q+(-1+\beta _{3})q^{2}-q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots\)
555.2.c.a	\(2\)	\(4.432\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+2iq^{2}+iq^{3}-2q^{4}+(-1+2i)q^{5}+\cdots\)
555.2.c.b	\(8\)	\(4.432\)	8.0.309760000.3	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
555.2.c.c	\(26\)	\(4.432\)		None	None	\(0\)	\(0\)	\(-2\)	\(0\)
555.2.e.a	\(2\)	\(4.432\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(-2\)	\(0\)	\(-8\)		\(q-q^{3}+2q^{4}+iq^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
555.2.e.b	\(10\)	\(4.432\)	10.0.\(\cdots\).1	None	None	\(0\)	\(10\)	\(0\)	\(16\)		\(q+\beta _{3}q^{2}+q^{3}+(-1+\beta _{1})q^{4}+\beta _{6}q^{5}+\cdots\)
555.2.e.c	\(12\)	\(4.432\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(-12\)	\(0\)	\(8\)		\(q-\beta _{8}q^{2}-q^{3}+(-2-\beta _{7})q^{4}+\beta _{2}q^{5}+\cdots\)
555.2.g.a	\(40\)	\(4.432\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
555.2.i.a	\(2\)	\(4.432\)	\(\Q(\sqrt{-3}) \)	None	None	\(-1\)	\(-1\)	\(1\)	\(-1\)		\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
555.2.i.b	\(4\)	\(4.432\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	None	\(-2\)	\(-2\)	\(2\)	\(2\)		\(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
555.2.i.c	\(4\)	\(4.432\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(-2\)	\(2\)	\(-2\)		\(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{3}+(-1+\cdots)q^{4}+\cdots\)
555.2.i.d	\(10\)	\(4.432\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	None	\(1\)	\(-5\)	\(-5\)	\(-1\)		\(q+(-\beta _{1}+\beta _{2})q^{2}-\beta _{6}q^{3}+(\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
555.2.i.e	\(14\)	\(4.432\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	None	\(-1\)	\(7\)	\(-7\)	\(5\)		\(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{4}+\beta _{5}+\beta _{7})q^{4}+\cdots\)
555.2.i.f	\(14\)	\(4.432\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	None	\(-1\)	\(7\)	\(7\)	\(1\)		\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{3}-\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots\)
555.2.j.a	\(76\)	\(4.432\)		None	None	\(0\)	\(0\)	\(4\)	\(0\)
555.2.m.a	\(16\)	\(4.432\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{3}-\beta _{10})q^{3}-2\beta _{9}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
555.2.m.b	\(128\)	\(4.432\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
555.2.n.a	\(32\)	\(4.432\)		\(\Q(\sqrt{-111}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)
555.2.n.b	\(112\)	\(4.432\)		None	None	\(0\)	\(-8\)	\(0\)	\(-8\)
555.2.o.a	\(144\)	\(4.432\)		None	None	\(0\)	\(0\)	\(0\)	\(-8\)
555.2.s.a	\(104\)	\(4.432\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
555.2.t.a	\(76\)	\(4.432\)		None	None	\(-4\)	\(0\)	\(-8\)	\(0\)
555.2.x.a	\(80\)	\(4.432\)		None	None	\(0\)	\(0\)	\(-12\)	\(0\)
555.2.z.a	\(20\)	\(4.432\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(6\)	\(-10\)	\(0\)	\(2\)		\(q-\beta _{4}q^{2}+(-1-\beta _{2})q^{3}+(\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
555.2.z.b	\(28\)	\(4.432\)		None	None	\(6\)	\(14\)	\(0\)	\(-6\)
555.2.bb.a	\(72\)	\(4.432\)		None	None	\(0\)	\(0\)	\(-2\)	\(0\)
555.2.bc.a	\(6\)	\(4.432\)	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(0\)	\(0\)	\(3\)		\(q-\zeta_{18}^{2}q^{3}+2\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
555.2.bc.b	\(36\)	\(4.432\)		None	None	\(3\)	\(0\)	\(0\)	\(12\)
555.2.bc.c	\(36\)	\(4.432\)		None	None	\(3\)	\(0\)	\(0\)	\(-6\)
555.2.bc.d	\(36\)	\(4.432\)		None	None	\(3\)	\(0\)	\(0\)	\(0\)
555.2.bc.e	\(42\)	\(4.432\)		None	None	\(3\)	\(0\)	\(0\)	\(-3\)
555.2.bd.a	\(152\)	\(4.432\)		None	None	\(4\)	\(0\)	\(8\)	\(0\)
555.2.bg.a	\(208\)	\(4.432\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
555.2.bh.a	\(288\)	\(4.432\)		None	None	\(0\)	\(-4\)	\(0\)	\(-4\)
555.2.bi.a	\(288\)	\(4.432\)		None	None	\(0\)	\(0\)	\(0\)	\(-4\)
555.2.bm.a	\(288\)	\(4.432\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
555.2.bn.a	\(152\)	\(4.432\)		None	None	\(0\)	\(0\)	\(-4\)	\(0\)
555.2.bp.a	\(240\)	\(4.432\)		None	None	\(0\)	\(0\)	\(12\)	\(0\)
555.2.bs.a	\(216\)	\(4.432\)		None	None	\(0\)	\(0\)	\(6\)	\(0\)
555.2.bt.a	\(72\)	\(4.432\)		None	None	\(-6\)	\(0\)	\(0\)	\(-12\)

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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.