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 82 matches)

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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
41.2.a.a	$3$	$0.327$	3.3.148.1	None	$-1$	$0$	$-2$	$6$	$-$	$q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
41.2.b.a	$2$	$0.327$	$\Q(\sqrt{-2}) $	None	$-2$	$0$	$4$	$0$		$q-q^{2}+\beta q^{3}-q^{4}+2q^{5}-\beta q^{6}-\beta q^{7}+\cdots$
41.2.c.a	$6$	$0.327$	6.0.5089536.1	None	$0$	$-4$	$0$	$-2$		$q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots$
41.2.d.a	$8$	$0.327$	8.0.13140625.1	None	$-1$	$-6$	$3$	$-3$		$q+(-\beta _{2}-\beta _{7})q^{2}+(-1+\beta _{5})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
41.2.f.a	$8$	$0.327$	$\Q(\zeta_{15})$	None	$-3$	$0$	$-9$	$-5$		$q+(-1-\zeta_{15}-\zeta_{15}^{5}-\zeta_{15}^{6})q^{2}+\cdots$
41.2.g.a	$24$	$0.327$		None	$-10$	$-6$	$-10$	$-8$
41.3.e.a	$4$	$1.117$	$\Q(\zeta_{8})$	None	$0$	$0$	$8$	$0$		$q-\zeta_{8}q^{2}+(-2\zeta_{8}+2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots$
41.3.e.b	$20$	$1.117$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$-8$	$4$	$-12$	$-4$		$q-\beta _{12}q^{2}-\beta _{8}q^{3}+(-\beta _{1}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
41.3.h.a	$96$	$1.117$		None	$-12$	$-24$	$-16$	$-16$
41.4.a.a	$3$	$2.419$	3.3.404.1	None	$-3$	$-8$	$-10$	$-50$	$-$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-3-\beta _{1}+2\beta _{2})q^{3}+\cdots$
41.4.a.b	$7$	$2.419$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$1$	$4$	$10$	$48$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6})q^{3}+(6+\beta _{1}+\cdots)q^{4}+\cdots$
41.4.b.a	$10$	$2.419$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$-6$	$0$	$-4$	$0$		$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+(4+\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots$
41.4.c.a	$2$	$2.419$	$\Q(\sqrt{-1}) $	None	$0$	$-4$	$0$	$50$		$q-iq^{2}+(-2+2i)q^{3}+7q^{4}+18iq^{5}+\cdots$
41.4.c.b	$16$	$2.419$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$0$	$-52$		$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(-5+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
41.4.d.a	$40$	$2.419$		None	$-3$	$-6$	$-5$	$-3$
41.4.f.a	$40$	$2.419$		None	$1$	$0$	$-1$	$-5$
41.4.g.a	$72$	$2.419$		None	$-10$	$-6$	$-10$	$-8$
41.5.e.a	$52$	$4.238$		None	$-4$	$-20$	$-4$	$-4$
41.5.h.a	$208$	$4.238$		None	$-16$	$0$	$-16$	$-16$
41.6.a.a	$6$	$6.576$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-5$	$-8$	$-68$	$-344$	$+$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots$
41.6.a.b	$10$	$6.576$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$3$	$28$	$32$	$342$	$-$	$q+\beta _{1}q^{2}+(3-\beta _{4})q^{3}+(21-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
41.6.b.a	$2$	$6.576$	$\Q(\sqrt{-2}) $	None	$-2$	$0$	$64$	$0$		$q-q^{2}+3\beta q^{3}-31q^{4}+2^{5}q^{5}-3\beta q^{6}+\cdots$
41.6.b.b	$14$	$6.576$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None	$8$	$0$	$-32$	$0$		$q+(1+\beta _{3})q^{2}-\beta _{1}q^{3}+(20+\beta _{4})q^{4}+\cdots$
41.6.c.a	$34$	$6.576$		None	$0$	$20$	$0$	$-2$
41.6.d.a	$64$	$6.576$		None	$-3$	$-30$	$31$	$-3$
41.6.f.a	$64$	$6.576$		None	$-11$	$0$	$-37$	$-5$
41.6.g.a	$136$	$6.576$		None	$-10$	$-30$	$-10$	$-8$
41.7.e.a	$80$	$9.432$		None	$12$	$-44$	$-4$	$-4$
41.7.h.a	$320$	$9.432$		None	$-32$	$24$	$-16$	$-16$
41.8.a.a	$10$	$12.808$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-1$	$-68$	$-320$	$-2402$	$-$	$q-\beta _{1}q^{2}+(-7+\beta _{3})q^{3}+(38+\beta _{1}+\cdots)q^{4}+\cdots$
41.8.a.b	$14$	$12.808$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$15$	$40$	$180$	$2400$	$+$	$q+(1+\beta _{1})q^{2}+(3+\beta _{4})q^{3}+(82+\beta _{1}+\cdots)q^{4}+\cdots$
41.8.b.a	$24$	$12.808$		None	$-2$	$0$	$136$	$0$
41.8.c.a	$46$	$12.808$		None	$0$	$-28$	$0$	$-2$
41.8.d.a	$96$	$12.808$		None	$-19$	$18$	$135$	$-3$
41.8.f.a	$96$	$12.808$		None	$-3$	$0$	$-141$	$-5$
41.8.g.a	$184$	$12.808$		None	$-10$	$18$	$-10$	$-8$
41.9.e.a	$108$	$16.703$		None	$-4$	$220$	$-4$	$-4$
41.9.h.a	$432$	$16.703$		None	$-16$	$-240$	$-16$	$-16$
41.10.a.a	$13$	$21.116$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	$-33$	$-236$	$-738$	$-16808$	$+$	$q+(-3+\beta _{1})q^{2}+(-18-\beta _{3})q^{3}+(160+\cdots)q^{4}+\cdots$
41.10.a.b	$17$	$21.116$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	$-1$	$88$	$1762$	$16806$	$-$	$q-\beta _{1}q^{2}+(5-\beta _{1}+\beta _{3})q^{3}+(301+\beta _{2}+\cdots)q^{4}+\cdots$
41.10.b.a	$30$	$21.116$		None	$-2$	$0$	$-1028$	$0$
41.10.c.a	$62$	$21.116$		None	$0$	$-148$	$0$	$-2$
41.10.d.a	$120$	$21.116$		None	$29$	$138$	$-1029$	$-3$
41.10.f.a	$120$	$21.116$		None	$-3$	$0$	$1023$	$-5$
41.10.g.a	$248$	$21.116$		None	$-10$	$138$	$-10$	$-8$
41.11.e.a	$136$	$26.050$		None	$-68$	$-92$	$-4$	$-4$
41.11.h.a	$544$	$26.050$		None	$48$	$72$	$-16$	$-16$
41.12.a.a	$16$	$31.502$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-9$	$-476$	$-2740$	$-100906$	$-$	$q+(-1+\beta _{1})q^{2}+(-29-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots$
41.12.a.b	$20$	$31.502$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$55$	$496$	$9760$	$134392$	$+$	$q+(3-\beta _{1})q^{2}+(5^{2}-\beta _{3})q^{3}+(1354+\cdots)q^{4}+\cdots$
41.12.b.a	$38$	$31.502$		None	$-66$	$0$	$-16684$	$0$

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Classical	Maass
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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	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
41.2.a.a	\(3\)	\(0.327\)	3.3.148.1	None	\(-1\)	\(0\)	\(-2\)	\(6\)	\(-\)	\(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
41.2.b.a	\(2\)	\(0.327\)	\(\Q(\sqrt{-2}) \)	None	\(-2\)	\(0\)	\(4\)	\(0\)		\(q-q^{2}+\beta q^{3}-q^{4}+2q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
41.2.c.a	\(6\)	\(0.327\)	6.0.5089536.1	None	\(0\)	\(-4\)	\(0\)	\(-2\)		\(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
41.2.d.a	\(8\)	\(0.327\)	8.0.13140625.1	None	\(-1\)	\(-6\)	\(3\)	\(-3\)		\(q+(-\beta _{2}-\beta _{7})q^{2}+(-1+\beta _{5})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
41.2.f.a	\(8\)	\(0.327\)	\(\Q(\zeta_{15})\)	None	\(-3\)	\(0\)	\(-9\)	\(-5\)		\(q+(-1-\zeta_{15}-\zeta_{15}^{5}-\zeta_{15}^{6})q^{2}+\cdots\)
41.2.g.a	\(24\)	\(0.327\)		None	\(-10\)	\(-6\)	\(-10\)	\(-8\)
41.3.e.a	\(4\)	\(1.117\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(8\)	\(0\)		\(q-\zeta_{8}q^{2}+(-2\zeta_{8}+2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots\)
41.3.e.b	\(20\)	\(1.117\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(-8\)	\(4\)	\(-12\)	\(-4\)		\(q-\beta _{12}q^{2}-\beta _{8}q^{3}+(-\beta _{1}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
41.3.h.a	\(96\)	\(1.117\)		None	\(-12\)	\(-24\)	\(-16\)	\(-16\)
41.4.a.a	\(3\)	\(2.419\)	3.3.404.1	None	\(-3\)	\(-8\)	\(-10\)	\(-50\)	\(-\)	\(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-3-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
41.4.a.b	\(7\)	\(2.419\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(1\)	\(4\)	\(10\)	\(48\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6})q^{3}+(6+\beta _{1}+\cdots)q^{4}+\cdots\)
41.4.b.a	\(10\)	\(2.419\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(-6\)	\(0\)	\(-4\)	\(0\)		\(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+(4+\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots\)
41.4.c.a	\(2\)	\(2.419\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(-4\)	\(0\)	\(50\)		\(q-iq^{2}+(-2+2i)q^{3}+7q^{4}+18iq^{5}+\cdots\)
41.4.c.b	\(16\)	\(2.419\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-52\)		\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(-5+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
41.4.d.a	\(40\)	\(2.419\)		None	\(-3\)	\(-6\)	\(-5\)	\(-3\)
41.4.f.a	\(40\)	\(2.419\)		None	\(1\)	\(0\)	\(-1\)	\(-5\)
41.4.g.a	\(72\)	\(2.419\)		None	\(-10\)	\(-6\)	\(-10\)	\(-8\)
41.5.e.a	\(52\)	\(4.238\)		None	\(-4\)	\(-20\)	\(-4\)	\(-4\)
41.5.h.a	\(208\)	\(4.238\)		None	\(-16\)	\(0\)	\(-16\)	\(-16\)
41.6.a.a	\(6\)	\(6.576\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-5\)	\(-8\)	\(-68\)	\(-344\)	\(+\)	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
41.6.a.b	\(10\)	\(6.576\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(3\)	\(28\)	\(32\)	\(342\)	\(-\)	\(q+\beta _{1}q^{2}+(3-\beta _{4})q^{3}+(21-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
41.6.b.a	\(2\)	\(6.576\)	\(\Q(\sqrt{-2}) \)	None	\(-2\)	\(0\)	\(64\)	\(0\)		\(q-q^{2}+3\beta q^{3}-31q^{4}+2^{5}q^{5}-3\beta q^{6}+\cdots\)
41.6.b.b	\(14\)	\(6.576\)	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None	\(8\)	\(0\)	\(-32\)	\(0\)		\(q+(1+\beta _{3})q^{2}-\beta _{1}q^{3}+(20+\beta _{4})q^{4}+\cdots\)
41.6.c.a	\(34\)	\(6.576\)		None	\(0\)	\(20\)	\(0\)	\(-2\)
41.6.d.a	\(64\)	\(6.576\)		None	\(-3\)	\(-30\)	\(31\)	\(-3\)
41.6.f.a	\(64\)	\(6.576\)		None	\(-11\)	\(0\)	\(-37\)	\(-5\)
41.6.g.a	\(136\)	\(6.576\)		None	\(-10\)	\(-30\)	\(-10\)	\(-8\)
41.7.e.a	\(80\)	\(9.432\)		None	\(12\)	\(-44\)	\(-4\)	\(-4\)
41.7.h.a	\(320\)	\(9.432\)		None	\(-32\)	\(24\)	\(-16\)	\(-16\)
41.8.a.a	\(10\)	\(12.808\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-1\)	\(-68\)	\(-320\)	\(-2402\)	\(-\)	\(q-\beta _{1}q^{2}+(-7+\beta _{3})q^{3}+(38+\beta _{1}+\cdots)q^{4}+\cdots\)
41.8.a.b	\(14\)	\(12.808\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(15\)	\(40\)	\(180\)	\(2400\)	\(+\)	\(q+(1+\beta _{1})q^{2}+(3+\beta _{4})q^{3}+(82+\beta _{1}+\cdots)q^{4}+\cdots\)
41.8.b.a	\(24\)	\(12.808\)		None	\(-2\)	\(0\)	\(136\)	\(0\)
41.8.c.a	\(46\)	\(12.808\)		None	\(0\)	\(-28\)	\(0\)	\(-2\)
41.8.d.a	\(96\)	\(12.808\)		None	\(-19\)	\(18\)	\(135\)	\(-3\)
41.8.f.a	\(96\)	\(12.808\)		None	\(-3\)	\(0\)	\(-141\)	\(-5\)
41.8.g.a	\(184\)	\(12.808\)		None	\(-10\)	\(18\)	\(-10\)	\(-8\)
41.9.e.a	\(108\)	\(16.703\)		None	\(-4\)	\(220\)	\(-4\)	\(-4\)
41.9.h.a	\(432\)	\(16.703\)		None	\(-16\)	\(-240\)	\(-16\)	\(-16\)
41.10.a.a	\(13\)	\(21.116\)	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	\(-33\)	\(-236\)	\(-738\)	\(-16808\)	\(+\)	\(q+(-3+\beta _{1})q^{2}+(-18-\beta _{3})q^{3}+(160+\cdots)q^{4}+\cdots\)
41.10.a.b	\(17\)	\(21.116\)	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	\(-1\)	\(88\)	\(1762\)	\(16806\)	\(-\)	\(q-\beta _{1}q^{2}+(5-\beta _{1}+\beta _{3})q^{3}+(301+\beta _{2}+\cdots)q^{4}+\cdots\)
41.10.b.a	\(30\)	\(21.116\)		None	\(-2\)	\(0\)	\(-1028\)	\(0\)
41.10.c.a	\(62\)	\(21.116\)		None	\(0\)	\(-148\)	\(0\)	\(-2\)
41.10.d.a	\(120\)	\(21.116\)		None	\(29\)	\(138\)	\(-1029\)	\(-3\)
41.10.f.a	\(120\)	\(21.116\)		None	\(-3\)	\(0\)	\(1023\)	\(-5\)
41.10.g.a	\(248\)	\(21.116\)		None	\(-10\)	\(138\)	\(-10\)	\(-8\)
41.11.e.a	\(136\)	\(26.050\)		None	\(-68\)	\(-92\)	\(-4\)	\(-4\)
41.11.h.a	\(544\)	\(26.050\)		None	\(48\)	\(72\)	\(-16\)	\(-16\)
41.12.a.a	\(16\)	\(31.502\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-9\)	\(-476\)	\(-2740\)	\(-100906\)	\(-\)	\(q+(-1+\beta _{1})q^{2}+(-29-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
41.12.a.b	\(20\)	\(31.502\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(55\)	\(496\)	\(9760\)	\(134392\)	\(+\)	\(q+(3-\beta _{1})q^{2}+(5^{2}-\beta _{3})q^{3}+(1354+\cdots)q^{4}+\cdots\)
41.12.b.a	\(38\)	\(31.502\)		None	\(-66\)	\(0\)	\(-16684\)	\(0\)

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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.