Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 25, -w^{3} + 5w + 3]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $39$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 29x^{7} - 18x^{6} + 239x^{5} + 275x^{4} - 441x^{3} - 669x^{2} - 27x + 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-\frac{139}{1545}e^{8} + \frac{244}{1545}e^{7} + \frac{3659}{1545}e^{6} - \frac{1348}{515}e^{5} - \frac{9193}{515}e^{4} + \frac{4132}{515}e^{3} + \frac{10151}{309}e^{2} - \frac{1039}{515}e - \frac{747}{103}$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $-\frac{7}{103}e^{8} + \frac{128}{1545}e^{7} + \frac{2887}{1545}e^{6} - \frac{1598}{1545}e^{5} - \frac{23042}{1545}e^{4} - \frac{1852}{1545}e^{3} + \frac{46898}{1545}e^{2} + \frac{1411}{103}e - \frac{4482}{515}$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $\phantom{-}\frac{139}{1545}e^{8} - \frac{244}{1545}e^{7} - \frac{3659}{1545}e^{6} + \frac{1348}{515}e^{5} + \frac{9193}{515}e^{4} - \frac{4132}{515}e^{3} - \frac{10151}{309}e^{2} + \frac{1554}{515}e + \frac{850}{103}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{1545}e^{8} + \frac{13}{515}e^{7} - \frac{52}{515}e^{6} - \frac{283}{515}e^{5} + \frac{922}{515}e^{4} + \frac{4531}{1545}e^{3} - \frac{2671}{309}e^{2} - \frac{1004}{515}e + \frac{819}{103}$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $\phantom{-}\frac{23}{1545}e^{8} - \frac{2}{103}e^{7} - \frac{601}{1545}e^{6} + \frac{91}{309}e^{5} + \frac{1327}{515}e^{4} - \frac{1259}{1545}e^{3} - \frac{637}{1545}e^{2} + \frac{1113}{515}e - \frac{3562}{515}$ |
| 23 | $[23, 23, -w^{3} + 4w + 2]$ | $-\frac{118}{515}e^{8} + \frac{511}{1545}e^{7} + \frac{3164}{515}e^{6} - \frac{7321}{1545}e^{5} - \frac{73382}{1545}e^{4} + \frac{8903}{1545}e^{3} + \frac{47164}{515}e^{2} + \frac{9851}{515}e - \frac{11853}{515}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}\frac{106}{309}e^{8} - \frac{217}{515}e^{7} - \frac{14494}{1545}e^{6} + \frac{8071}{1545}e^{5} + \frac{114929}{1545}e^{4} + \frac{7504}{1545}e^{3} - \frac{229886}{1545}e^{2} - \frac{5175}{103}e + \frac{20019}{515}$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{118}{515}e^{8} - \frac{511}{1545}e^{7} - \frac{3164}{515}e^{6} + \frac{7321}{1545}e^{5} + \frac{73382}{1545}e^{4} - \frac{8903}{1545}e^{3} - \frac{47164}{515}e^{2} - \frac{10366}{515}e + \frac{11853}{515}$ |
| 29 | $[29, 29, -w + 3]$ | $\phantom{-}\frac{91}{309}e^{8} - \frac{589}{1545}e^{7} - \frac{12476}{1545}e^{6} + \frac{2663}{515}e^{5} + \frac{33157}{515}e^{4} - \frac{3854}{1545}e^{3} - \frac{67753}{515}e^{2} - \frac{2887}{103}e + \frac{21276}{515}$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}\frac{112}{309}e^{8} - \frac{239}{515}e^{7} - \frac{5121}{515}e^{6} + \frac{9587}{1545}e^{5} + \frac{122513}{1545}e^{4} - \frac{2002}{1545}e^{3} - \frac{250157}{1545}e^{2} - \frac{4195}{103}e + \frac{25758}{515}$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $\phantom{-}\frac{139}{1545}e^{8} - \frac{244}{1545}e^{7} - \frac{3659}{1545}e^{6} + \frac{1348}{515}e^{5} + \frac{9193}{515}e^{4} - \frac{4132}{515}e^{3} - \frac{9842}{309}e^{2} + \frac{1039}{515}e + \frac{232}{103}$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $\phantom{-}\frac{49}{309}e^{8} - \frac{111}{515}e^{7} - \frac{2234}{515}e^{6} + \frac{4793}{1545}e^{5} + \frac{53387}{1545}e^{4} - \frac{6013}{1545}e^{3} - \frac{109463}{1545}e^{2} - \frac{1507}{103}e + \frac{8707}{515}$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $-\frac{797}{1545}e^{8} + \frac{351}{515}e^{7} + \frac{21641}{1545}e^{6} - \frac{14168}{1545}e^{5} - \frac{169531}{1545}e^{4} + \frac{1433}{515}e^{3} + \frac{109907}{515}e^{2} + \frac{30263}{515}e - \frac{25704}{515}$ |
| 59 | $[59, 59, w^{2} + w - 4]$ | $-\frac{231}{515}e^{8} + \frac{886}{1545}e^{7} + \frac{3782}{309}e^{6} - \frac{3907}{515}e^{5} - \frac{29851}{309}e^{4} + \frac{5}{103}e^{3} + \frac{98726}{515}e^{2} + \frac{30907}{515}e - \frac{25317}{515}$ |
| 61 | $[61, 61, -2w^{2} + w + 8]$ | $-\frac{316}{1545}e^{8} + \frac{23}{103}e^{7} + \frac{2939}{515}e^{6} - \frac{263}{103}e^{5} - \frac{23964}{515}e^{4} - \frac{8542}{1545}e^{3} + \frac{150959}{1545}e^{2} + \frac{15989}{515}e - \frac{12391}{515}$ |
| 73 | $[73, 73, -w^{3} + 5w - 1]$ | $-\frac{1012}{1545}e^{8} + \frac{88}{103}e^{7} + \frac{9158}{515}e^{6} - \frac{1163}{103}e^{5} - \frac{71778}{515}e^{4} + \frac{806}{1545}e^{3} + \frac{418913}{1545}e^{2} + \frac{41668}{515}e - \frac{31762}{515}$ |
| 79 | $[79, 79, 2w^{2} + w - 6]$ | $-\frac{1036}{1545}e^{8} + \frac{437}{515}e^{7} + \frac{28231}{1545}e^{6} - \frac{17051}{1545}e^{5} - \frac{74027}{515}e^{4} - \frac{822}{515}e^{3} + \frac{86890}{309}e^{2} + \frac{40529}{515}e - \frac{7077}{103}$ |
| 79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $\phantom{-}\frac{251}{1545}e^{8} - \frac{202}{1545}e^{7} - \frac{468}{103}e^{6} + \frac{449}{515}e^{5} + \frac{11195}{309}e^{4} + \frac{1233}{103}e^{3} - \frac{103691}{1545}e^{2} - \frac{17164}{515}e + \frac{3304}{515}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^{2} + w + 2]$ | $1$ |