Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} + 2w + 4]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 41x^{8} + 533x^{6} - 2360x^{4} + 1552x^{2} - 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $-\frac{149}{24944}e^{8} + \frac{5693}{24944}e^{6} - \frac{66201}{24944}e^{4} + \frac{30289}{3118}e^{2} - \frac{1896}{1559}$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{139}{24944}e^{8} + \frac{5855}{24944}e^{6} - \frac{79043}{24944}e^{4} + \frac{89921}{6236}e^{2} - \frac{8643}{1559}$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{427}{49888}e^{9} + \frac{17403}{49888}e^{7} - \frac{224287}{49888}e^{5} + \frac{30832}{1559}e^{3} - \frac{42567}{3118}e$ |
| 17 | $[17, 17, -w - 3]$ | $-\frac{97}{24944}e^{8} + \frac{4041}{24944}e^{6} - \frac{55653}{24944}e^{4} + \frac{34555}{3118}e^{2} - \frac{9542}{1559}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{97}{49888}e^{9} - \frac{4041}{49888}e^{7} + \frac{55653}{49888}e^{5} - \frac{37673}{6236}e^{3} + \frac{15684}{1559}e$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}\frac{203}{12472}e^{9} - \frac{1031}{1559}e^{7} + \frac{13287}{1559}e^{5} - \frac{472501}{12472}e^{3} + \frac{89151}{3118}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{705}{49888}e^{9} - \frac{29113}{49888}e^{7} + \frac{382373}{49888}e^{5} - \frac{213249}{6236}e^{3} + \frac{62971}{3118}e$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{2}{1559}e^{8} - \frac{247}{3118}e^{6} + \frac{4529}{3118}e^{4} - \frac{25077}{3118}e^{2} + \frac{8966}{1559}$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $-\frac{20}{1559}e^{8} + \frac{3381}{6236}e^{6} - \frac{45369}{6236}e^{4} + \frac{200653}{6236}e^{2} - \frac{14828}{1559}$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-\frac{77}{49888}e^{9} + \frac{4365}{49888}e^{7} - \frac{81337}{49888}e^{5} + \frac{16754}{1559}e^{3} - \frac{25549}{1559}e$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $-\frac{875}{24944}e^{9} + \frac{35713}{24944}e^{7} - \frac{460269}{24944}e^{5} + \frac{994963}{12472}e^{3} - \frac{122599}{3118}e$ |
| 31 | $[31, 31, w^{2} - 2]$ | $\phantom{-}\frac{1365}{49888}e^{9} - \frac{55837}{49888}e^{7} + \frac{719641}{49888}e^{5} - \frac{384559}{6236}e^{3} + \frac{88487}{3118}e$ |
| 37 | $[37, 37, 2w - 5]$ | $\phantom{-}\frac{19}{1559}e^{9} - \frac{1567}{3118}e^{7} + \frac{10210}{1559}e^{5} - \frac{43894}{1559}e^{3} + \frac{28485}{3118}e$ |
| 43 | $[43, 43, w^{2} - 2w - 5]$ | $\phantom{-}\frac{181}{12472}e^{8} - \frac{7669}{12472}e^{6} + \frac{102433}{12472}e^{4} - \frac{55366}{1559}e^{2} + \frac{21724}{1559}$ |
| 47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}\frac{191}{12472}e^{8} - \frac{7507}{12472}e^{6} + \frac{89591}{12472}e^{4} - \frac{81389}{3118}e^{2} + \frac{5112}{1559}$ |
| 49 | $[49, 7, w^{2} + w - 4]$ | $-\frac{951}{49888}e^{9} + \frac{38847}{49888}e^{7} - \frac{504227}{49888}e^{5} + \frac{284329}{6236}e^{3} - \frac{61369}{1559}e$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}\frac{175}{12472}e^{8} - \frac{6519}{12472}e^{6} + \frac{71475}{12472}e^{4} - \frac{29715}{1559}e^{2} + \frac{8618}{1559}$ |
| 71 | $[71, 71, w - 5]$ | $-\frac{5}{6236}e^{8} - \frac{81}{6236}e^{6} + \frac{6421}{6236}e^{4} - \frac{26225}{3118}e^{2} + \frac{4140}{1559}$ |
Atkin-Lehner eigenvalues
The Atkin-Lehner eigenvalues for this form are not in the database.