Base field 4.4.10889.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{3} + w^{2} + 5w]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 28x^{14} + 315x^{12} - 1824x^{10} + 5790x^{8} - 9923x^{6} + 8378x^{4} - 2725x^{2} + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 2]$ | $-\frac{356}{82491}e^{15} + \frac{11483}{82491}e^{13} - \frac{49112}{27497}e^{11} + \frac{314844}{27497}e^{9} - \frac{1028702}{27497}e^{7} + \frac{4503088}{82491}e^{5} - \frac{1511191}{82491}e^{3} - \frac{866254}{82491}e$ |
| 8 | $[8, 2, -w^{3} + 5w + 3]$ | $-\frac{521}{54994}e^{15} + \frac{6433}{27497}e^{13} - \frac{117685}{54994}e^{11} + \frac{229420}{27497}e^{9} - \frac{222141}{27497}e^{7} - \frac{1704323}{54994}e^{5} + \frac{2160124}{27497}e^{3} - \frac{2578181}{54994}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 5w + 4]$ | $\phantom{-}\frac{355}{27497}e^{14} - \frac{7975}{27497}e^{12} + \frac{65358}{27497}e^{10} - \frac{225721}{27497}e^{8} + \frac{215432}{27497}e^{6} + \frac{411751}{27497}e^{4} - \frac{735218}{27497}e^{2} + \frac{177786}{27497}$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{237}{27497}e^{15} - \frac{6486}{27497}e^{13} + \frac{70898}{27497}e^{11} - \frac{399250}{27497}e^{9} + \frac{1256329}{27497}e^{7} - \frac{2243683}{27497}e^{5} + \frac{2091791}{27497}e^{3} - \frac{715204}{27497}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $-1$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $\phantom{-}\frac{3509}{164982}e^{15} - \frac{50452}{82491}e^{13} + \frac{389853}{54994}e^{11} - \frac{1169954}{27497}e^{9} + \frac{3895255}{27497}e^{7} - \frac{42836983}{164982}e^{5} + \frac{19606211}{82491}e^{3} - \frac{12838313}{164982}e$ |
| 25 | $[25, 5, -w^{2} + 2]$ | $-\frac{185}{2661}e^{15} + \frac{5018}{2661}e^{13} - \frac{18037}{887}e^{11} + \frac{98493}{887}e^{9} - \frac{287190}{887}e^{7} + \frac{1296049}{2661}e^{5} - \frac{878572}{2661}e^{3} + \frac{192890}{2661}e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $\phantom{-}\frac{964}{27497}e^{15} - \frac{27078}{27497}e^{13} + \frac{302881}{27497}e^{11} - \frac{1714218}{27497}e^{9} + \frac{5146098}{27497}e^{7} - \frac{7815862}{27497}e^{5} + \frac{5153980}{27497}e^{3} - \frac{1166811}{27497}e$ |
| 29 | $[29, 29, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{1793}{27497}e^{15} - \frac{48025}{27497}e^{13} + \frac{510035}{27497}e^{11} - \frac{2738439}{27497}e^{9} + \frac{7874188}{27497}e^{7} - \frac{11891477}{27497}e^{5} + \frac{8574847}{27497}e^{3} - \frac{2281948}{27497}e$ |
| 37 | $[37, 37, 4w^{3} - 2w^{2} - 21w - 4]$ | $-\frac{1098}{27497}e^{14} + \frac{29701}{27497}e^{12} - \frac{316630}{27497}e^{10} + \frac{1685404}{27497}e^{8} - \frac{4665935}{27497}e^{6} + \frac{6228815}{27497}e^{4} - \frac{2798385}{27497}e^{2} - \frac{265310}{27497}$ |
| 43 | $[43, 43, 4w^{3} - 2w^{2} - 20w - 3]$ | $\phantom{-}\frac{47}{164982}e^{15} + \frac{53}{82491}e^{13} - \frac{8037}{54994}e^{11} + \frac{56610}{27497}e^{9} - \frac{353895}{27497}e^{7} + \frac{6906611}{164982}e^{5} - \frac{5544274}{82491}e^{3} + \frac{6318337}{164982}e$ |
| 47 | $[47, 47, -w^{3} + 6w]$ | $-\frac{1139}{54994}e^{15} + \frac{18022}{27497}e^{13} - \frac{460579}{54994}e^{11} + \frac{1513612}{27497}e^{9} - \frac{5376623}{27497}e^{7} + \frac{19740225}{54994}e^{5} - \frac{8074873}{27497}e^{3} + \frac{4256429}{54994}e$ |
| 53 | $[53, 53, w^{3} - w^{2} - 5w - 2]$ | $-\frac{3191}{27497}e^{14} + \frac{85240}{27497}e^{12} - \frac{892741}{27497}e^{10} + \frac{4628148}{27497}e^{8} - \frac{12316307}{27497}e^{6} + \frac{15653128}{27497}e^{4} - \frac{7219912}{27497}e^{2} + \frac{26421}{27497}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{3413}{27497}e^{14} - \frac{94100}{27497}e^{12} + \frac{1026328}{27497}e^{10} - \frac{5601494}{27497}e^{8} + \frac{15882576}{27497}e^{6} - \frac{21743263}{27497}e^{4} + \frac{11086698}{27497}e^{2} - \frac{592288}{27497}$ |
| 83 | $[83, 83, 2w^{3} - w^{2} - 10w - 4]$ | $-\frac{2330}{27497}e^{14} + \frac{62025}{27497}e^{12} - \frac{647009}{27497}e^{10} + \frac{3341994}{27497}e^{8} - \frac{8879204}{27497}e^{6} + \frac{11338032}{27497}e^{4} - \frac{5495929}{27497}e^{2} + \frac{511989}{27497}$ |
| 89 | $[89, 89, w^{3} - 2w^{2} - 4w + 2]$ | $-\frac{66}{887}e^{14} + \frac{1795}{887}e^{12} - \frac{19362}{887}e^{10} + \frac{104997}{887}e^{8} - \frac{297542}{887}e^{6} + \frac{406172}{887}e^{4} - \frac{190762}{887}e^{2} - \frac{4974}{887}$ |
| 89 | $[89, 89, 2w - 3]$ | $-\frac{2243}{54994}e^{15} + \frac{29648}{27497}e^{13} - \frac{609149}{54994}e^{11} + \frac{1515574}{27497}e^{9} - \frac{3631747}{27497}e^{7} + \frac{6265941}{54994}e^{5} + \frac{1481027}{27497}e^{3} - \frac{4759185}{54994}e$ |
| 101 | $[101, 101, 6w^{3} - 3w^{2} - 31w - 5]$ | $\phantom{-}\frac{679}{27497}e^{14} - \frac{17190}{27497}e^{12} + \frac{174116}{27497}e^{10} - \frac{908320}{27497}e^{8} + \frac{2592525}{27497}e^{6} - \frac{3851856}{27497}e^{4} + \frac{2390366}{27497}e^{2} - \frac{144210}{27497}$ |
| 107 | $[107, 107, -w^{3} + w^{2} + 4w - 5]$ | $-\frac{774}{27497}e^{14} + \frac{20486}{27497}e^{12} - \frac{207872}{27497}e^{10} + \frac{1002805}{27497}e^{8} - \frac{2288842}{27497}e^{6} + \frac{2020202}{27497}e^{4} - \frac{57759}{27497}e^{2} - \frac{477318}{27497}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{3} + w^{2} + 5w]$ | $1$ |