Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ |
| Dimension: | $61$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $106$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{61} - 13x^{60} - 46x^{59} + 1293x^{58} - 1313x^{57} - 58307x^{56} + 173521x^{55} + 1555970x^{54} - 7138745x^{53} - 26525310x^{52} + 177834244x^{51} + 277007017x^{50} - 3093831601x^{49} - 1054963001x^{48} + 39954222163x^{47} - 19291324963x^{46} - 395272103155x^{45} + 445574870139x^{44} + 3043716038986x^{43} - 5196846427269x^{42} - 18322721784609x^{41} + 42448949626429x^{40} + 85515349111758x^{39} - 263578435281740x^{38} - 300184551203463x^{37} + 1286013764705955x^{36} + 722792302115189x^{35} - 5006886633559445x^{34} - 746614092584545x^{33} + 15659134223920609x^{32} - 2588787600495275x^{31} - 39388237085155109x^{30} + 16452626508475450x^{29} + 79449042102926491x^{28} - 50126759771116683x^{27} - 127659486555115555x^{26} + 104861960366417934x^{25} + 161714945271303308x^{24} - 162201341596916033x^{23} - 159177578041720300x^{22} + 189376518760177995x^{21} + 119441484604547309x^{20} - 167016095075677676x^{19} - 66726399070694759x^{18} + 110117605653120674x^{17} + 27056339399900605x^{16} - 53252712578179810x^{15} - 7850992929569225x^{14} + 18361405121791569x^{13} + 1691888224583922x^{12} - 4329657201988607x^{11} - 308272972755295x^{10} + 653042593979410x^{9} + 50294174750339x^{8} - 55659724523934x^{7} - 5665781428281x^{6} + 1985689138743x^{5} + 276940296902x^{4} - 197886878x^{3} - 1423382320x^{2} - 67981396x - 933928\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $...$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $...$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $...$ |
| 17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $...$ |
| 31 | $[31, 31, w^{3} - 4w + 2]$ | $...$ |
| 32 | $[32, 2, 2]$ | $...$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $...$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $...$ |
| 59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $...$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $...$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $\phantom{-}1$ |
| 71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $...$ |
| 79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $...$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $...$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $...$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $...$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $67$ | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $-1$ |