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 matches 1-50 of 80) Next

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
29.2.a.a	$2$	$0.232$	$\Q(\sqrt{2}) $	None	$-2$	$2$	$-2$	$0$	$-$	$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
29.2.b.a	$2$	$0.232$	$\Q(\sqrt{-5}) $	None	$0$	$0$	$-6$	$4$		$q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots$
29.2.d.a	$6$	$0.232$	$\Q(\zeta_{14})$	None	$-2$	$-5$	$1$	$1$		$q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
29.2.e.a	$12$	$0.232$	12.0.$\cdots$.1	None	$-7$	$-7$	$-1$	$-11$		$q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots$
29.3.c.a	$8$	$0.790$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$2$	$-2$	$0$	$-4$		$q-\beta _{6}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
29.3.f.a	$48$	$0.790$		None	$-16$	$-12$	$-14$	$-10$
29.4.a.a	$2$	$1.711$	$\Q(\sqrt{2}) $	None	$-2$	$-10$	$-10$	$-16$	$-$	$q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots$
29.4.a.b	$5$	$1.711$	5.5.13458092.1	None	$0$	$8$	$10$	$40$	$+$	$q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots$
29.4.b.a	$6$	$1.711$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None	$0$	$0$	$22$	$-28$		$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-5+\beta _{4}+\beta _{5})q^{4}+\cdots$
29.4.d.a	$42$	$1.711$		None	$-5$	$-5$	$-7$	$-31$
29.4.e.a	$36$	$1.711$		None	$-7$	$-7$	$-29$	$21$
29.5.c.a	$18$	$2.998$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$-8$	$-2$	$0$	$-4$		$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{2}+6\beta _{4}+\cdots)q^{4}+\cdots$
29.5.f.a	$108$	$2.998$		None	$-6$	$-12$	$-14$	$-10$
29.6.a.a	$4$	$4.651$	4.4.3257317.1	None	$0$	$-28$	$-68$	$-208$	$+$	$q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots$
29.6.a.b	$7$	$4.651$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$4$	$26$	$32$	$184$	$-$	$q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots$
29.6.b.a	$12$	$4.651$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$46$	$20$		$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-14+\beta _{2})q^{4}+\cdots$
29.6.d.a	$66$	$4.651$		None	$-11$	$-5$	$29$	$17$
29.6.e.a	$72$	$4.651$		None	$-7$	$-7$	$-53$	$-27$
29.7.c.a	$28$	$6.672$		None	$0$	$-2$	$0$	$-4$
29.7.f.a	$168$	$6.672$		None	$-14$	$-12$	$-14$	$-10$
29.8.a.a	$7$	$9.059$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$-8$	$-82$	$-320$	$-1704$	$-$	$q+(-1-\beta _{1})q^{2}+(-12+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
29.8.a.b	$10$	$9.059$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$80$	$180$	$1040$	$+$	$q-\beta _{1}q^{2}+(8+\beta _{2})q^{3}+(92+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
29.8.b.a	$16$	$9.059$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$-198$	$660$		$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(-45+\beta _{2}+\cdots)q^{4}+\cdots$
29.8.d.a	$102$	$9.059$		None	$1$	$-5$	$133$	$657$
29.8.e.a	$96$	$9.059$		None	$-7$	$-7$	$191$	$-667$
29.9.c.a	$38$	$11.814$		None	$-8$	$-2$	$0$	$-4$
29.9.f.a	$228$	$11.814$		None	$-6$	$-12$	$-14$	$-10$
29.10.a.a	$9$	$14.936$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$-244$	$-738$	$-7128$	$+$	$q-\beta _{1}q^{2}+(-3^{3}-\beta _{4})q^{3}+(133+2\beta _{1}+\cdots)q^{4}+\cdots$
29.10.a.b	$12$	$14.936$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$16$	$242$	$1762$	$12080$	$-$	$q+(1+\beta _{1})q^{2}+(20+\beta _{1}-\beta _{3})q^{3}+(291+\cdots)q^{4}+\cdots$
29.10.b.a	$22$	$14.936$		None	$0$	$0$	$-1374$	$-4956$
29.10.d.a	$126$	$14.936$		None	$-23$	$-5$	$-1031$	$-4959$
29.10.e.a	$132$	$14.936$		None	$-7$	$-7$	$1367$	$4949$
29.11.c.a	$48$	$18.425$		None	$8$	$-2$	$0$	$-4$
29.11.f.a	$288$	$18.425$		None	$-22$	$-12$	$-14$	$-10$
29.12.a.a	$11$	$22.282$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	$-32$	$-982$	$-2740$	$-49432$	$-$	$q+(-3+\beta _{1})q^{2}+(-89-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots$
29.12.a.b	$14$	$22.282$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$0$	$476$	$9760$	$85024$	$+$	$q+\beta _{1}q^{2}+(34-\beta _{3})q^{3}+(1312+3\beta _{1}+\cdots)q^{4}+\cdots$
29.12.b.a	$26$	$22.282$		None	$0$	$0$	$3742$	$-2108$
29.12.d.a	$162$	$22.282$		None	$73$	$-5$	$-16687$	$-2111$
29.12.e.a	$156$	$22.282$		None	$-7$	$-7$	$-3749$	$2101$
29.13.c.a	$58$	$26.506$		None	$88$	$-2$	$0$	$-4$
29.14.a.a	$14$	$31.097$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$0$	$-2188$	$-67808$	$-669728$	$+$	$q+\beta _{1}q^{2}+(-156-\beta _{1}+\beta _{3})q^{3}+(2912+\cdots)q^{4}+\cdots$
29.14.a.b	$17$	$31.097$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	$64$	$2186$	$-5308$	$271464$	$-$	$q+(4-\beta _{1})q^{2}+(129-\beta _{1}+\beta _{3})q^{3}+\cdots$
29.14.b.a	$32$	$31.097$		None	$0$	$0$	$-90794$	$398260$
29.15.c.a	$68$	$36.055$		None	$-312$	$-2$	$0$	$-4$
29.16.a.a	$16$	$41.381$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-128$	$-3214$	$-82010$	$-3706320$	$-$	$q+(-8-\beta _{1})q^{2}+(-201+\beta _{2})q^{3}+\cdots$
29.16.a.b	$19$	$41.381$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	$0$	$9908$	$230490$	$2882024$	$+$	$q+\beta _{1}q^{2}+(521+2\beta _{1}+\beta _{2})q^{3}+(20389+\cdots)q^{4}+\cdots$
29.16.b.a	$36$	$41.381$		None	$0$	$0$	$470082$	$-4820620$
29.17.c.a	$78$	$47.074$		None	$184$	$-2$	$0$	$-4$
29.18.a.a	$18$	$53.134$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$0$	$-15400$	$-564228$	$-43925040$	$+$	$q+\beta _{1}q^{2}+(-856-2\beta _{1}+\beta _{2})q^{3}+\cdots$
29.18.a.b	$21$	$53.134$		None	$256$	$23966$	$998272$	$2193368$	$-$

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
29.2.a.a	\(2\)	\(0.232\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
29.2.b.a	\(2\)	\(0.232\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(-6\)	\(4\)		\(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)
29.2.d.a	\(6\)	\(0.232\)	\(\Q(\zeta_{14})\)	None	\(-2\)	\(-5\)	\(1\)	\(1\)		\(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
29.2.e.a	\(12\)	\(0.232\)	12.0.\(\cdots\).1	None	\(-7\)	\(-7\)	\(-1\)	\(-11\)		\(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)
29.3.c.a	\(8\)	\(0.790\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(2\)	\(-2\)	\(0\)	\(-4\)		\(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
29.3.f.a	\(48\)	\(0.790\)		None	\(-16\)	\(-12\)	\(-14\)	\(-10\)
29.4.a.a	\(2\)	\(1.711\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(-10\)	\(-10\)	\(-16\)	\(-\)	\(q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
29.4.a.b	\(5\)	\(1.711\)	5.5.13458092.1	None	\(0\)	\(8\)	\(10\)	\(40\)	\(+\)	\(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots\)
29.4.b.a	\(6\)	\(1.711\)	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None	\(0\)	\(0\)	\(22\)	\(-28\)		\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-5+\beta _{4}+\beta _{5})q^{4}+\cdots\)
29.4.d.a	\(42\)	\(1.711\)		None	\(-5\)	\(-5\)	\(-7\)	\(-31\)
29.4.e.a	\(36\)	\(1.711\)		None	\(-7\)	\(-7\)	\(-29\)	\(21\)
29.5.c.a	\(18\)	\(2.998\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(-8\)	\(-2\)	\(0\)	\(-4\)		\(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{2}+6\beta _{4}+\cdots)q^{4}+\cdots\)
29.5.f.a	\(108\)	\(2.998\)		None	\(-6\)	\(-12\)	\(-14\)	\(-10\)
29.6.a.a	\(4\)	\(4.651\)	4.4.3257317.1	None	\(0\)	\(-28\)	\(-68\)	\(-208\)	\(+\)	\(q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.a.b	\(7\)	\(4.651\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(4\)	\(26\)	\(32\)	\(184\)	\(-\)	\(q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.b.a	\(12\)	\(4.651\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(46\)	\(20\)		\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-14+\beta _{2})q^{4}+\cdots\)
29.6.d.a	\(66\)	\(4.651\)		None	\(-11\)	\(-5\)	\(29\)	\(17\)
29.6.e.a	\(72\)	\(4.651\)		None	\(-7\)	\(-7\)	\(-53\)	\(-27\)
29.7.c.a	\(28\)	\(6.672\)		None	\(0\)	\(-2\)	\(0\)	\(-4\)
29.7.f.a	\(168\)	\(6.672\)		None	\(-14\)	\(-12\)	\(-14\)	\(-10\)
29.8.a.a	\(7\)	\(9.059\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(-8\)	\(-82\)	\(-320\)	\(-1704\)	\(-\)	\(q+(-1-\beta _{1})q^{2}+(-12+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
29.8.a.b	\(10\)	\(9.059\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(80\)	\(180\)	\(1040\)	\(+\)	\(q-\beta _{1}q^{2}+(8+\beta _{2})q^{3}+(92+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
29.8.b.a	\(16\)	\(9.059\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(-198\)	\(660\)		\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(-45+\beta _{2}+\cdots)q^{4}+\cdots\)
29.8.d.a	\(102\)	\(9.059\)		None	\(1\)	\(-5\)	\(133\)	\(657\)
29.8.e.a	\(96\)	\(9.059\)		None	\(-7\)	\(-7\)	\(191\)	\(-667\)
29.9.c.a	\(38\)	\(11.814\)		None	\(-8\)	\(-2\)	\(0\)	\(-4\)
29.9.f.a	\(228\)	\(11.814\)		None	\(-6\)	\(-12\)	\(-14\)	\(-10\)
29.10.a.a	\(9\)	\(14.936\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(-244\)	\(-738\)	\(-7128\)	\(+\)	\(q-\beta _{1}q^{2}+(-3^{3}-\beta _{4})q^{3}+(133+2\beta _{1}+\cdots)q^{4}+\cdots\)
29.10.a.b	\(12\)	\(14.936\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(16\)	\(242\)	\(1762\)	\(12080\)	\(-\)	\(q+(1+\beta _{1})q^{2}+(20+\beta _{1}-\beta _{3})q^{3}+(291+\cdots)q^{4}+\cdots\)
29.10.b.a	\(22\)	\(14.936\)		None	\(0\)	\(0\)	\(-1374\)	\(-4956\)
29.10.d.a	\(126\)	\(14.936\)		None	\(-23\)	\(-5\)	\(-1031\)	\(-4959\)
29.10.e.a	\(132\)	\(14.936\)		None	\(-7\)	\(-7\)	\(1367\)	\(4949\)
29.11.c.a	\(48\)	\(18.425\)		None	\(8\)	\(-2\)	\(0\)	\(-4\)
29.11.f.a	\(288\)	\(18.425\)		None	\(-22\)	\(-12\)	\(-14\)	\(-10\)
29.12.a.a	\(11\)	\(22.282\)	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	\(-32\)	\(-982\)	\(-2740\)	\(-49432\)	\(-\)	\(q+(-3+\beta _{1})q^{2}+(-89-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
29.12.a.b	\(14\)	\(22.282\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(0\)	\(476\)	\(9760\)	\(85024\)	\(+\)	\(q+\beta _{1}q^{2}+(34-\beta _{3})q^{3}+(1312+3\beta _{1}+\cdots)q^{4}+\cdots\)
29.12.b.a	\(26\)	\(22.282\)		None	\(0\)	\(0\)	\(3742\)	\(-2108\)
29.12.d.a	\(162\)	\(22.282\)		None	\(73\)	\(-5\)	\(-16687\)	\(-2111\)
29.12.e.a	\(156\)	\(22.282\)		None	\(-7\)	\(-7\)	\(-3749\)	\(2101\)
29.13.c.a	\(58\)	\(26.506\)		None	\(88\)	\(-2\)	\(0\)	\(-4\)
29.14.a.a	\(14\)	\(31.097\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(0\)	\(-2188\)	\(-67808\)	\(-669728\)	\(+\)	\(q+\beta _{1}q^{2}+(-156-\beta _{1}+\beta _{3})q^{3}+(2912+\cdots)q^{4}+\cdots\)
29.14.a.b	\(17\)	\(31.097\)	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	\(64\)	\(2186\)	\(-5308\)	\(271464\)	\(-\)	\(q+(4-\beta _{1})q^{2}+(129-\beta _{1}+\beta _{3})q^{3}+\cdots\)
29.14.b.a	\(32\)	\(31.097\)		None	\(0\)	\(0\)	\(-90794\)	\(398260\)
29.15.c.a	\(68\)	\(36.055\)		None	\(-312\)	\(-2\)	\(0\)	\(-4\)
29.16.a.a	\(16\)	\(41.381\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-128\)	\(-3214\)	\(-82010\)	\(-3706320\)	\(-\)	\(q+(-8-\beta _{1})q^{2}+(-201+\beta _{2})q^{3}+\cdots\)
29.16.a.b	\(19\)	\(41.381\)	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	\(0\)	\(9908\)	\(230490\)	\(2882024\)	\(+\)	\(q+\beta _{1}q^{2}+(521+2\beta _{1}+\beta _{2})q^{3}+(20389+\cdots)q^{4}+\cdots\)
29.16.b.a	\(36\)	\(41.381\)		None	\(0\)	\(0\)	\(470082\)	\(-4820620\)
29.17.c.a	\(78\)	\(47.074\)		None	\(184\)	\(-2\)	\(0\)	\(-4\)
29.18.a.a	\(18\)	\(53.134\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(0\)	\(-15400\)	\(-564228\)	\(-43925040\)	\(+\)	\(q+\beta _{1}q^{2}+(-856-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
29.18.a.b	\(21\)	\(53.134\)		None	\(256\)	\(23966\)	\(998272\)	\(2193368\)	\(-\)

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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.