Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} - w + 6]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 58x^{8} + 1260x^{6} - 12535x^{4} + 55548x^{2} - 87723\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{32}{6165}e^{8} - \frac{1118}{6165}e^{6} + \frac{1187}{685}e^{4} - \frac{12563}{6165}e^{2} - \frac{8379}{685}$ |
| 11 | $[11, 11, w + 2]$ | $-\frac{356}{351405}e^{9} + \frac{13979}{351405}e^{7} - \frac{21511}{39045}e^{5} + \frac{1126934}{351405}e^{3} - \frac{250568}{39045}e$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{224}{70281}e^{9} - \frac{9059}{70281}e^{7} + \frac{13652}{7809}e^{5} - \frac{631694}{70281}e^{3} + \frac{35249}{2603}e$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $\phantom{-}e$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $-\frac{2}{411}e^{9} + \frac{29}{137}e^{7} - \frac{1327}{411}e^{5} + \frac{8363}{411}e^{3} - \frac{18808}{411}e$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}\frac{224}{70281}e^{9} - \frac{9059}{70281}e^{7} + \frac{13652}{7809}e^{5} - \frac{631694}{70281}e^{3} + \frac{35249}{2603}e$ |
| 23 | $[23, 23, -w + 4]$ | $-\frac{53}{6165}e^{8} + \frac{2237}{6165}e^{6} - \frac{3443}{685}e^{4} + \frac{152777}{6165}e^{2} - \frac{24204}{685}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{23}{2055}e^{8} - \frac{932}{2055}e^{6} + \frac{4379}{685}e^{4} - \frac{76652}{2055}e^{2} + \frac{51182}{685}$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $\phantom{-}\frac{2}{1233}e^{8} - \frac{224}{1233}e^{6} + \frac{665}{137}e^{4} - \frac{54806}{1233}e^{2} + \frac{15942}{137}$ |
| 31 | $[31, 31, w^{2} - 10]$ | $-\frac{35}{1233}e^{8} + \frac{1454}{1233}e^{6} - \frac{2253}{137}e^{4} + \frac{108335}{1233}e^{2} - \frac{21562}{137}$ |
| 41 | $[41, 41, w + 4]$ | $\phantom{-}\frac{19}{1233}e^{8} - \frac{895}{1233}e^{6} + \frac{1591}{137}e^{4} - \frac{89107}{1233}e^{2} + \frac{19929}{137}$ |
| 41 | $[41, 41, w^{2} - 5]$ | $-\frac{29}{39045}e^{9} + \frac{371}{39045}e^{7} + \frac{5528}{13015}e^{5} - \frac{307204}{39045}e^{3} + \frac{346764}{13015}e$ |
| 41 | $[41, 41, -2w - 5]$ | $\phantom{-}\frac{11}{18495}e^{9} + \frac{1}{18495}e^{7} - \frac{1069}{2055}e^{5} + \frac{133816}{18495}e^{3} - \frac{15709}{685}e$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}\frac{7}{70281}e^{9} + \frac{449}{70281}e^{7} - \frac{617}{2603}e^{5} + \frac{116429}{70281}e^{3} - \frac{6538}{7809}e$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}\frac{1}{3699}e^{9} - \frac{112}{3699}e^{7} + \frac{401}{411}e^{5} - \frac{40966}{3699}e^{3} + \frac{13999}{411}e$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $-\frac{566}{70281}e^{9} + \frac{23936}{70281}e^{7} - \frac{12955}{2603}e^{5} + \frac{2061767}{70281}e^{3} - \frac{463099}{7809}e$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $-\frac{559}{70281}e^{9} + \frac{24385}{70281}e^{7} - \frac{13572}{2603}e^{5} + \frac{2178196}{70281}e^{3} - \frac{469637}{7809}e$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{217}{70281}e^{9} - \frac{9508}{70281}e^{7} + \frac{15503}{7809}e^{5} - \frac{818404}{70281}e^{3} + \frac{221611}{7809}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w + 2]$ | $1$ |