Base field 5.5.122821.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[23, 23, w^{4} - 3w^{3} - w^{2} + 5w - 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 6x^{9} - 11x^{8} - 114x^{7} - 37x^{6} + 650x^{5} + 591x^{4} - 1009x^{3} - 851x^{2} + 281x + 181\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{4} - 2w^{3} - 3w^{2} + 2w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $\phantom{-}\frac{8352}{51427}e^{9} + \frac{23159}{51427}e^{8} - \frac{164805}{51427}e^{7} - \frac{420373}{51427}e^{6} + \frac{985908}{51427}e^{5} + \frac{2186039}{51427}e^{4} - \frac{1614942}{51427}e^{3} - \frac{2586555}{51427}e^{2} + \frac{263762}{51427}e + \frac{457658}{51427}$ |
| 11 | $[11, 11, -w^{2} + w + 2]$ | $-\frac{4691}{51427}e^{9} - \frac{15920}{51427}e^{8} + \frac{85342}{51427}e^{7} + \frac{299326}{51427}e^{6} - \frac{426140}{51427}e^{5} - \frac{1656330}{51427}e^{4} + \frac{312205}{51427}e^{3} + \frac{2313562}{51427}e^{2} + \frac{218260}{51427}e - \frac{509098}{51427}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $-\frac{3004}{51427}e^{9} - \frac{9241}{51427}e^{8} + \frac{56690}{51427}e^{7} + \frac{173044}{51427}e^{6} - \frac{317070}{51427}e^{5} - \frac{980468}{51427}e^{4} + \frac{450069}{51427}e^{3} + \frac{1583130}{51427}e^{2} - \frac{52850}{51427}e - \frac{624446}{51427}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + w - 3]$ | $-\frac{729}{51427}e^{9} - \frac{1301}{51427}e^{8} + \frac{13997}{51427}e^{7} + \frac{17684}{51427}e^{6} - \frac{64996}{51427}e^{5} - \frac{5659}{51427}e^{4} - \frac{45796}{51427}e^{3} - \frac{447717}{51427}e^{2} + \frac{207845}{51427}e + \frac{259638}{51427}$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 3w^{2} + w + 2]$ | $-\frac{8352}{51427}e^{9} - \frac{23159}{51427}e^{8} + \frac{164805}{51427}e^{7} + \frac{420373}{51427}e^{6} - \frac{985908}{51427}e^{5} - \frac{2186039}{51427}e^{4} + \frac{1614942}{51427}e^{3} + \frac{2586555}{51427}e^{2} - \frac{315189}{51427}e - \frac{560512}{51427}$ |
| 23 | $[23, 23, w^{4} - 3w^{3} - w^{2} + 5w - 3]$ | $-1$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{6077}{51427}e^{9} - \frac{15219}{51427}e^{8} + \frac{122112}{51427}e^{7} + \frac{265013}{51427}e^{6} - \frac{785261}{51427}e^{5} - \frac{1314084}{51427}e^{4} + \frac{1633347}{51427}e^{3} + \frac{1429967}{51427}e^{2} - \frac{517337}{51427}e - \frac{242125}{51427}$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 4w - 1]$ | $\phantom{-}\frac{14876}{51427}e^{9} + \frac{39599}{51427}e^{8} - \frac{301002}{51427}e^{7} - \frac{725858}{51427}e^{6} + \frac{1889327}{51427}e^{5} + \frac{3835223}{51427}e^{4} - \frac{3584430}{51427}e^{3} - \frac{4750854}{51427}e^{2} + \frac{1435430}{51427}e + \frac{1004059}{51427}$ |
| 37 | $[37, 37, w^{4} - 3w^{3} - w^{2} + 5w]$ | $-\frac{7612}{51427}e^{9} - \frac{14925}{51427}e^{8} + \frac{163577}{51427}e^{7} + \frac{261333}{51427}e^{6} - \frac{1132341}{51427}e^{5} - \frac{1289246}{51427}e^{4} + \frac{2603693}{51427}e^{3} + \frac{1391131}{51427}e^{2} - \frac{1248194}{51427}e - \frac{522278}{51427}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 4w^{2} + 3w + 1]$ | $\phantom{-}\frac{11577}{51427}e^{9} + \frac{36110}{51427}e^{8} - \frac{217414}{51427}e^{7} - \frac{642304}{51427}e^{6} + \frac{1216089}{51427}e^{5} + \frac{3271782}{51427}e^{4} - \frac{1741437}{51427}e^{3} - \frac{3819784}{51427}e^{2} + \frac{291979}{51427}e + \frac{811230}{51427}$ |
| 49 | $[49, 7, -2w^{3} + 4w^{2} + 6w - 5]$ | $\phantom{-}\frac{3874}{51427}e^{9} + \frac{10582}{51427}e^{8} - \frac{70643}{51427}e^{7} - \frac{179334}{51427}e^{6} + \frac{355485}{51427}e^{5} + \frac{795693}{51427}e^{4} - \frac{239018}{51427}e^{3} - \frac{364394}{51427}e^{2} - \frac{534656}{51427}e - \frac{20003}{51427}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + w^{2} - 7w + 3]$ | $-\frac{10773}{51427}e^{9} - \frac{24940}{51427}e^{8} + \frac{229701}{51427}e^{7} + \frac{455610}{51427}e^{6} - \frac{1554764}{51427}e^{5} - \frac{2323559}{51427}e^{4} + \frac{3443111}{51427}e^{3} + \frac{2349178}{51427}e^{2} - \frac{1979787}{51427}e - \frac{465853}{51427}$ |
| 67 | $[67, 67, w^{3} - 2w^{2} - w + 3]$ | $\phantom{-}\frac{2546}{51427}e^{9} + \frac{1087}{51427}e^{8} - \frac{55374}{51427}e^{7} + \frac{8784}{51427}e^{6} + \frac{410341}{51427}e^{5} - \frac{297193}{51427}e^{4} - \frac{1159737}{51427}e^{3} + \frac{1257186}{51427}e^{2} + \frac{895084}{51427}e - \frac{697680}{51427}$ |
| 67 | $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 6w - 1]$ | $-\frac{19391}{51427}e^{9} - \frac{47445}{51427}e^{8} + \frac{384940}{51427}e^{7} + \frac{820568}{51427}e^{6} - \frac{2355576}{51427}e^{5} - \frac{3884451}{51427}e^{4} + \frac{4224366}{51427}e^{3} + \frac{3042051}{51427}e^{2} - \frac{1248655}{51427}e + \frac{64321}{51427}$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 4]$ | $-\frac{13482}{51427}e^{9} - \frac{39933}{51427}e^{8} + \frac{259493}{51427}e^{7} + \frac{718144}{51427}e^{6} - \frac{1515666}{51427}e^{5} - \frac{3721054}{51427}e^{4} + \frac{2500256}{51427}e^{3} + \frac{4532941}{51427}e^{2} - \frac{1096317}{51427}e - \frac{1007646}{51427}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 8w - 2]$ | $\phantom{-}\frac{10050}{51427}e^{9} + \frac{36771}{51427}e^{8} - \frac{180688}{51427}e^{7} - \frac{688011}{51427}e^{6} + \frac{883549}{51427}e^{5} + \frac{3753035}{51427}e^{4} - \frac{534123}{51427}e^{3} - \frac{5011555}{51427}e^{2} - \frac{629654}{51427}e + \frac{1257306}{51427}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 6w - 2]$ | $-\frac{2938}{51427}e^{9} - \frac{19070}{51427}e^{8} + \frac{30450}{51427}e^{7} + \frac{353448}{51427}e^{6} + \frac{111447}{51427}e^{5} - \frac{1959185}{51427}e^{4} - \frac{1503397}{51427}e^{3} + \frac{2935370}{51427}e^{2} + \frac{1356014}{51427}e - \frac{637159}{51427}$ |
| 103 | $[103, 103, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{23659}{51427}e^{9} - \frac{63245}{51427}e^{8} + \frac{470414}{51427}e^{7} + \frac{1154076}{51427}e^{6} - \frac{2861459}{51427}e^{5} - \frac{6060656}{51427}e^{4} + \frac{5032336}{51427}e^{3} + \frac{7360108}{51427}e^{2} - \frac{1655108}{51427}e - \frac{1753491}{51427}$ |
| 113 | $[113, 113, -2w^{4} + 4w^{3} + 7w^{2} - 7w - 2]$ | $-\frac{1748}{51427}e^{9} - \frac{3049}{51427}e^{8} + \frac{32645}{51427}e^{7} + \frac{54607}{51427}e^{6} - \frac{142797}{51427}e^{5} - \frac{241146}{51427}e^{4} - \frac{93373}{51427}e^{3} + \frac{1138}{51427}e^{2} + \frac{234394}{51427}e - \frac{157309}{51427}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, w^{4} - 3w^{3} - w^{2} + 5w - 3]$ | $1$ |