Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} + w + 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 10x^{7} - 5x^{6} + 292x^{5} - 664x^{4} - 596x^{3} + 1920x^{2} + 368x - 384\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $-\frac{6431}{862304}e^{7} + \frac{8969}{215576}e^{6} + \frac{237003}{862304}e^{5} - \frac{604849}{431152}e^{4} - \frac{467595}{215576}e^{3} + \frac{1613453}{215576}e^{2} + \frac{545175}{107788}e - \frac{21463}{26947}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{6645}{862304}e^{7} - \frac{14237}{215576}e^{6} - \frac{100513}{862304}e^{5} + \frac{856391}{431152}e^{4} - \frac{568017}{215576}e^{3} - \frac{1243399}{215576}e^{2} + \frac{530503}{107788}e + \frac{161777}{26947}$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{10563}{862304}e^{7} + \frac{23045}{215576}e^{6} + \frac{136127}{862304}e^{5} - \frac{1353693}{431152}e^{4} + \frac{1106753}{215576}e^{3} + \frac{1457393}{215576}e^{2} - \frac{1280969}{107788}e + \frac{20409}{26947}$ |
| 19 | $[19, 19, w^{3} - 5w]$ | $\phantom{-}\frac{2849}{862304}e^{7} - \frac{2831}{107788}e^{6} - \frac{53573}{862304}e^{5} + \frac{347861}{431152}e^{4} - \frac{200613}{215576}e^{3} - \frac{603871}{215576}e^{2} + \frac{566037}{107788}e + \frac{70622}{26947}$ |
| 19 | $[19, 19, -w + 3]$ | $-\frac{715}{107788}e^{7} + \frac{9599}{215576}e^{6} + \frac{18439}{107788}e^{5} - \frac{277935}{215576}e^{4} + \frac{4019}{107788}e^{3} + \frac{111351}{53894}e^{2} + \frac{317283}{53894}e + \frac{123623}{26947}$ |
| 23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $\phantom{-}\frac{901}{431152}e^{7} - \frac{791}{215576}e^{6} - \frac{55949}{431152}e^{5} + \frac{7321}{53894}e^{4} + \frac{265349}{107788}e^{3} - \frac{115705}{107788}e^{2} - \frac{319311}{26947}e - \frac{22278}{26947}$ |
| 23 | $[23, 23, w^{2} - 2]$ | $-\frac{10219}{862304}e^{7} + \frac{20621}{215576}e^{6} + \frac{210471}{862304}e^{5} - \frac{1247525}{431152}e^{4} + \frac{415145}{215576}e^{3} + \frac{1756081}{215576}e^{2} + \frac{148971}{107788}e - \frac{49701}{26947}$ |
| 25 | $[25, 5, w^{2} - 3]$ | $\phantom{-}\frac{1069}{431152}e^{7} - \frac{1573}{53894}e^{6} + \frac{17959}{431152}e^{5} + \frac{149441}{215576}e^{4} - \frac{338123}{107788}e^{3} + \frac{282089}{107788}e^{2} + \frac{292217}{53894}e - \frac{74464}{26947}$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $\phantom{-}\frac{5469}{431152}e^{7} - \frac{8457}{107788}e^{6} - \frac{186717}{431152}e^{5} + \frac{581179}{215576}e^{4} + \frac{71978}{26947}e^{3} - \frac{1710515}{107788}e^{2} - \frac{299553}{53894}e + \frac{284651}{26947}$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $\phantom{-}\frac{1791}{431152}e^{7} - \frac{3307}{215576}e^{6} - \frac{91715}{431152}e^{5} + \frac{64247}{107788}e^{4} + \frac{83526}{26947}e^{3} - \frac{504791}{107788}e^{2} - \frac{250856}{26947}e - \frac{49159}{26947}$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{23631}{862304}e^{7} - \frac{6166}{26947}e^{6} - \frac{400171}{862304}e^{5} + \frac{2949079}{431152}e^{4} - \frac{1722511}{215576}e^{3} - \frac{3817345}{215576}e^{2} + \frac{1698035}{107788}e + \frac{207702}{26947}$ |
| 47 | $[47, 47, w^{3} - 6w + 1]$ | $-\frac{3231}{215576}e^{7} + \frac{27775}{215576}e^{6} + \frac{58751}{215576}e^{5} - \frac{873233}{215576}e^{4} + \frac{418807}{107788}e^{3} + \frac{416531}{26947}e^{2} - \frac{591065}{53894}e - \frac{227379}{26947}$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{4745}{215576}e^{7} + \frac{42875}{215576}e^{6} + \frac{58675}{215576}e^{5} - \frac{1271325}{215576}e^{4} + \frac{513149}{53894}e^{3} + \frac{372758}{26947}e^{2} - \frac{1204621}{53894}e - \frac{159358}{26947}$ |
| 67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $-\frac{5633}{431152}e^{7} + \frac{6373}{53894}e^{6} + \frac{76073}{431152}e^{5} - \frac{768409}{215576}e^{4} + \frac{143307}{26947}e^{3} + \frac{1064271}{107788}e^{2} - \frac{954943}{53894}e - \frac{34813}{26947}$ |
| 67 | $[67, 67, w^{3} - 7w + 3]$ | $-\frac{275}{431152}e^{7} + \frac{10769}{215576}e^{6} - \frac{142153}{431152}e^{5} - \frac{30741}{26947}e^{4} + \frac{560639}{53894}e^{3} - \frac{582821}{107788}e^{2} - \frac{788233}{26947}e + \frac{46607}{26947}$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $\phantom{-}\frac{10391}{431152}e^{7} - \frac{21833}{107788}e^{6} - \frac{173299}{431152}e^{5} + \frac{1300609}{215576}e^{4} - \frac{760949}{107788}e^{3} - \frac{1606737}{107788}e^{2} + \frac{512105}{53894}e + \frac{244868}{26947}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{7603}{431152}e^{7} - \frac{32575}{215576}e^{6} - \frac{114063}{431152}e^{5} + \frac{473567}{107788}e^{4} - \frac{323001}{53894}e^{3} - \frac{790099}{107788}e^{2} + \frac{223428}{26947}e - \frac{277505}{26947}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 1]$ | $-1$ |
| $5$ | $[5, 5, -w + 2]$ | $-1$ |