Newform search results

Results (1-50 of 163 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.37.b.a	$3$	$37$	3.b	3.b	$2$	$1$	$1$	$24.627$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(387420489\)	\(0\)	\(27\!\cdots\!98\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\)
4.33.b.a	$4$	$33$	4.b	4.b	$2$	$1$	$1$	$25.947$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(65536\)	\(0\)	\(-196496109694\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{16}q^{2}+2^{32}q^{4}-196496109694q^{5}+\cdots\)
4.37.b.a	$4$	$37$	4.b	4.b	$2$	$1$	$1$	$32.837$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-262144\)	\(0\)	\(-42\!\cdots\!34\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{18}q^{2}+2^{36}q^{4}-4228490555534q^{5}+\cdots\)
3.43.b.a	$3$	$43$	3.b	3.b	$2$	$1$	$1$	$33.518$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-10460353203\)	\(0\)	\(14\!\cdots\!86\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{21}q^{3}+2^{42}q^{4}+146246101081752386q^{7}+\cdots\)
4.41.b.a	$4$	$41$	4.b	4.b	$2$	$1$	$1$	$40.537$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(1048576\)	\(0\)	\(18\!\cdots\!26\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{20}q^{2}+2^{40}q^{4}+182008936336226q^{5}+\cdots\)
3.49.b.a	$3$	$49$	3.b	3.b	$2$	$1$	$1$	$43.777$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(282429536481\)	\(0\)	\(-36\!\cdots\!98\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{24}q^{3}+2^{48}q^{4}-366190448997743510398q^{7}+\cdots\)
7.33.b.a	$7$	$33$	7.b	7.b	$2$	$1$	$1$	$45.407$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(70529\)	\(0\)	\(0\)	\(33\!\cdots\!01\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+70529q^{2}+679372545q^{4}+7^{16}q^{7}+\cdots\)
4.45.b.a	$4$	$45$	4.b	4.b	$2$	$1$	$1$	$49.048$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-4194304\)	\(0\)	\(94\!\cdots\!86\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{22}q^{2}+2^{44}q^{4}+94681488501586q^{5}+\cdots\)
7.35.b.a	$7$	$35$	7.b	7.b	$2$	$1$	$1$	$51.258$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-251943\)	\(0\)	\(0\)	\(-23\!\cdots\!07\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-251943q^{2}+46295406065q^{4}+\cdots\)
8.33.d.a	$8$	$33$	8.d	8.d	$2$	$1$	$1$	$51.893$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(65536\)	\(57091714\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{16}q^{2}+57091714q^{3}+2^{32}q^{4}+\cdots\)
3.55.b.a	$3$	$55$	3.b	3.b	$2$	$1$	$1$	$55.404$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-76\!\cdots\!87\)	\(0\)	\(87\!\cdots\!14\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{27}q^{3}+2^{54}q^{4}+87524760867187557513314q^{7}+\cdots\)
7.37.b.a	$7$	$37$	7.b	7.b	$2$	$1$	$1$	$57.464$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(473713\)	\(0\)	\(0\)	\(16\!\cdots\!49\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+473713q^{2}+155684529633q^{4}+\cdots\)
4.49.b.a	$4$	$49$	4.b	4.b	$2$	$1$	$1$	$58.369$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(16777216\)	\(0\)	\(-11\!\cdots\!54\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{24}q^{2}+2^{48}q^{4}-115081126049163454q^{5}+\cdots\)
8.35.d.a	$8$	$35$	8.d	8.d	$2$	$1$	$1$	$58.581$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-131072\)	\(125174398\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{17}q^{2}+125174398q^{3}+2^{34}q^{4}+\cdots\)
9.34.a.a	$9$	$34$	9.a	1.a	$1$	$1$	$1$	$62.085$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(15\!\cdots\!40\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{33}q^{4}+1589751452540q^{7}+\cdots\)
7.39.b.a	$7$	$39$	7.b	7.b	$2$	$1$	$1$	$64.024$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-413367\)	\(0\)	\(0\)	\(-11\!\cdots\!43\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-413367q^{2}-104005630255q^{4}+\cdots\)
8.37.d.a	$8$	$37$	8.d	8.d	$2$	$1$	$1$	$65.673$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(262144\)	\(-764174222\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{18}q^{2}-764174222q^{3}+2^{36}q^{4}+\cdots\)
3.61.b.a	$3$	$61$	3.b	3.b	$2$	$1$	$1$	$68.398$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(20\!\cdots\!49\)	\(0\)	\(18\!\cdots\!98\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{30}q^{3}+2^{60}q^{4}+18049858526119884806006498q^{7}+\cdots\)
4.53.b.a	$4$	$53$	4.b	4.b	$2$	$1$	$1$	$68.502$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-67108864\)	\(0\)	\(15\!\cdots\!06\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{26}q^{2}+2^{52}q^{4}+1551959834374797106q^{5}+\cdots\)
7.41.b.a	$7$	$41$	7.b	7.b	$2$	$1$	$1$	$70.940$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-654751\)	\(0\)	\(0\)	\(79\!\cdots\!01\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-654751q^{2}-670812755775q^{4}+\cdots\)
11.33.b.a	$11$	$33$	11.b	11.b	$2$	$1$	$1$	$71.353$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-85968833\)	\(-9728091649\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-85968833q^{3}+2^{32}q^{4}-9728091649q^{5}+\cdots\)
8.39.d.a	$8$	$39$	8.d	8.d	$2$	$1$	$1$	$73.171$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-524288\)	\(401778862\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{19}q^{2}+401778862q^{3}+2^{38}q^{4}+\cdots\)
12.33.c.a	$12$	$33$	12.c	3.b	$2$	$1$	$1$	$77.840$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(43046721\)	\(0\)	\(-43\!\cdots\!86\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{16}q^{3}-43964556588286q^{7}+\cdots\)
7.43.b.a	$7$	$43$	7.b	7.b	$2$	$1$	$1$	$78.209$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(3617721\)	\(0\)	\(0\)	\(-55\!\cdots\!07\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3617721q^{2}+8689858722737q^{4}+\cdots\)
4.57.b.a	$4$	$57$	4.b	4.b	$2$	$1$	$1$	$79.444$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(268435456\)	\(0\)	\(50\!\cdots\!66\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{28}q^{2}+2^{56}q^{4}+50198266099479999266q^{5}+\cdots\)
11.35.b.a	$11$	$35$	11.b	11.b	$2$	$1$	$1$	$80.548$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(222600715\)	\(-15\!\cdots\!01\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+222600715q^{3}+2^{34}q^{4}-1512594730201q^{5}+\cdots\)
8.41.d.a	$8$	$41$	8.d	8.d	$2$	$1$	$1$	$81.074$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(1048576\)	\(6074010274\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{20}q^{2}+6074010274q^{3}+2^{40}q^{4}+\cdots\)
7.45.b.a	$7$	$45$	7.b	7.b	$2$	$1$	$1$	$85.834$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-8234159\)	\(0\)	\(0\)	\(39\!\cdots\!49\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-8234159q^{2}+50209188392865q^{4}+\cdots\)
9.40.a.a	$9$	$40$	9.a	1.a	$1$	$1$	$1$	$86.706$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(54\!\cdots\!40\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{39}q^{4}+54595696320612740q^{7}+\cdots\)
12.35.c.a	$12$	$35$	12.c	3.b	$2$	$1$	$1$	$87.871$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-129140163\)	\(0\)	\(30\!\cdots\!42\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{17}q^{3}+301392890307842q^{7}+\cdots\)
8.43.d.a	$8$	$43$	8.d	8.d	$2$	$1$	$1$	$89.382$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-2097152\)	\(-15764030306\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{21}q^{2}-15764030306q^{3}+2^{42}q^{4}+\cdots\)
11.37.b.a	$11$	$37$	11.b	11.b	$2$	$1$	$1$	$90.300$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-339284078\)	\(17\!\cdots\!26\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-339284078q^{3}+2^{36}q^{4}+1755797021426q^{5}+\cdots\)
4.61.b.a	$4$	$61$	4.b	4.b	$2$	$1$	$1$	$91.198$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-1073741824\)	\(0\)	\(-16\!\cdots\!74\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{30}q^{2}+2^{60}q^{4}-1672750621876968180974q^{5}+\cdots\)
7.47.b.a	$7$	$47$	7.b	7.b	$2$	$1$	$1$	$93.813$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(10231593\)	\(0\)	\(0\)	\(-27\!\cdots\!43\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+10231593q^{2}+34316751139985q^{4}+\cdots\)
15.33.d.a	$15$	$33$	15.d	15.d	$2$	$1$	$1$	$97.300$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-81343\)	\(43046721\)	\(152587890625\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-81343q^{2}+3^{16}q^{3}+2321716353q^{4}+\cdots\)
15.33.d.b	$15$	$33$	15.d	15.d	$2$	$1$	$1$	$97.300$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(81343\)	\(-43046721\)	\(-152587890625\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+81343q^{2}-3^{16}q^{3}+2321716353q^{4}+\cdots\)
8.45.d.a	$8$	$45$	8.d	8.d	$2$	$1$	$1$	$98.096$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(4194304\)	\(-23138031854\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{22}q^{2}-23138031854q^{3}+2^{44}q^{4}+\cdots\)
11.39.b.a	$11$	$39$	11.b	11.b	$2$	$1$	$1$	$100.610$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-306986045\)	\(36\!\cdots\!99\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-306986045q^{3}+2^{38}q^{4}+36059071233599q^{5}+\cdots\)
7.49.b.a	$7$	$49$	7.b	7.b	$2$	$1$	$1$	$102.147$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(2241857\)	\(0\)	\(0\)	\(19\!\cdots\!01\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2241857q^{2}-276449053902207q^{4}+\cdots\)
8.47.d.a	$8$	$47$	8.d	8.d	$2$	$1$	$1$	$107.215$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-8388608\)	\(188152336462\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{23}q^{2}+188152336462q^{3}+2^{46}q^{4}+\cdots\)
12.39.c.a	$12$	$39$	12.c	3.b	$2$	$1$	$1$	$109.756$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-1162261467\)	\(0\)	\(-92\!\cdots\!62\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{19}q^{3}-9254153518200862q^{7}+\cdots\)
15.35.d.a	$15$	$35$	15.d	15.d	$2$	$1$	$1$	$109.838$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-239699\)	\(-129140163\)	\(762939453125\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-239699q^{2}-3^{17}q^{3}+40275741417q^{4}+\cdots\)
15.35.d.b	$15$	$35$	15.d	15.d	$2$	$1$	$1$	$109.838$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(239699\)	\(129140163\)	\(-762939453125\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+239699q^{2}+3^{17}q^{3}+40275741417q^{4}+\cdots\)
7.51.b.a	$7$	$51$	7.b	7.b	$2$	$1$	$1$	$110.835$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-47651943\)	\(0\)	\(0\)	\(-13\!\cdots\!07\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-47651943q^{2}+1144807764832625q^{4}+\cdots\)
11.41.b.a	$11$	$41$	11.b	11.b	$2$	$1$	$1$	$111.477$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(4588486927\)	\(-79\!\cdots\!49\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4588486927q^{3}+2^{40}q^{4}-79953996769249q^{5}+\cdots\)
9.46.a.a	$9$	$46$	9.a	1.a	$1$	$1$	$1$	$115.430$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-15\!\cdots\!00\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{45}q^{4}-15801401816335122100q^{7}+\cdots\)
8.49.d.a	$8$	$49$	8.d	8.d	$2$	$1$	$1$	$116.739$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(16777216\)	\(-168062386238\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{24}q^{2}-168062386238q^{3}+2^{48}q^{4}+\cdots\)
16.35.c.a	$16$	$35$	16.c	4.b	$2$	$1$	$1$	$117.161$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(15\!\cdots\!14\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+1523482216314q^{5}+3^{34}q^{9}+\cdots\)
7.53.b.a	$7$	$53$	7.b	7.b	$2$	$1$	$1$	$119.878$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(133988401\)	\(0\)	\(0\)	\(93\!\cdots\!49\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+133988401q^{2}+13449291975166305q^{4}+\cdots\)
12.41.c.a	$12$	$41$	12.c	3.b	$2$	$1$	$1$	$121.611$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(3486784401\)	\(0\)	\(-15\!\cdots\!26\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{20}q^{3}-153603710655044926q^{7}+\cdots\)