Base field 4.4.4400.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[49, 7, -w^{3} + w^{2} + 4w - 1]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 6x^{5} + 3x^{4} - 34x^{3} - 41x^{2} + 30x + 25\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{2}{5}e^{5} + \frac{7}{5}e^{4} - \frac{14}{5}e^{3} - \frac{43}{5}e^{2} + \frac{28}{5}e + 5$ |
5 | $[5, 5, -w^{3} + w^{2} + 4w - 4]$ | $-\frac{4}{5}e^{5} - \frac{14}{5}e^{4} + \frac{23}{5}e^{3} + \frac{76}{5}e^{2} - \frac{36}{5}e - 8$ |
11 | $[11, 11, w]$ | $\phantom{-}\frac{4}{5}e^{5} + \frac{14}{5}e^{4} - \frac{18}{5}e^{3} - \frac{71}{5}e^{2} + \frac{6}{5}e + 5$ |
29 | $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{6}{5}e^{4} + \frac{3}{5}e^{3} - \frac{34}{5}e^{2} - \frac{26}{5}e + 8$ |
29 | $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ | $\phantom{-}\frac{7}{5}e^{5} + \frac{22}{5}e^{4} - \frac{44}{5}e^{3} - \frac{128}{5}e^{2} + \frac{53}{5}e + 16$ |
31 | $[31, 31, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{6}{5}e^{5} - \frac{21}{5}e^{4} + \frac{32}{5}e^{3} + \frac{114}{5}e^{2} - \frac{44}{5}e - 15$ |
31 | $[31, 31, -w^{3} - w^{2} + 4w + 2]$ | $\phantom{-}\frac{7}{5}e^{5} + \frac{22}{5}e^{4} - \frac{44}{5}e^{3} - \frac{118}{5}e^{2} + \frac{68}{5}e + 4$ |
41 | $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ | $-\frac{4}{5}e^{5} - \frac{14}{5}e^{4} + \frac{23}{5}e^{3} + \frac{86}{5}e^{2} - \frac{16}{5}e - 14$ |
41 | $[41, 41, w^{3} - 5w + 2]$ | $\phantom{-}\frac{2}{5}e^{5} + \frac{7}{5}e^{4} - \frac{14}{5}e^{3} - \frac{48}{5}e^{2} + \frac{18}{5}e + 4$ |
49 | $[49, 7, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}1$ |
49 | $[49, 7, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}\frac{6}{5}e^{5} + \frac{21}{5}e^{4} - \frac{32}{5}e^{3} - \frac{104}{5}e^{2} + \frac{44}{5}e + 3$ |
59 | $[59, 59, -3w^{2} - w + 10]$ | $\phantom{-}\frac{2}{5}e^{5} + \frac{2}{5}e^{4} - \frac{24}{5}e^{3} - \frac{3}{5}e^{2} + \frac{88}{5}e + 1$ |
59 | $[59, 59, -3w^{2} + w + 10]$ | $\phantom{-}\frac{2}{5}e^{5} + \frac{12}{5}e^{4} + \frac{1}{5}e^{3} - \frac{68}{5}e^{2} - \frac{47}{5}e + 6$ |
61 | $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ | $-\frac{2}{5}e^{5} - \frac{7}{5}e^{4} + \frac{4}{5}e^{3} + \frac{33}{5}e^{2} + \frac{22}{5}e - 8$ |
61 | $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ | $-\frac{9}{5}e^{5} - \frac{24}{5}e^{4} + \frac{68}{5}e^{3} + \frac{136}{5}e^{2} - \frac{131}{5}e - 14$ |
71 | $[71, 71, 2w^{2} + w - 9]$ | $-\frac{11}{5}e^{5} - \frac{36}{5}e^{4} + \frac{77}{5}e^{3} + \frac{214}{5}e^{2} - \frac{154}{5}e - 26$ |
71 | $[71, 71, 2w^{2} - w - 9]$ | $-\frac{11}{5}e^{5} - \frac{36}{5}e^{4} + \frac{57}{5}e^{3} + \frac{184}{5}e^{2} - \frac{54}{5}e - 16$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{6}{5}e^{5} + \frac{26}{5}e^{4} - \frac{22}{5}e^{3} - \frac{139}{5}e^{2} + \frac{14}{5}e + 15$ |
101 | $[101, 101, 2w^{2} - w - 10]$ | $\phantom{-}\frac{6}{5}e^{5} + \frac{21}{5}e^{4} - \frac{32}{5}e^{3} - \frac{99}{5}e^{2} + \frac{54}{5}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$49$ | $[49, 7, -w^{3} + w^{2} + 4w - 1]$ | $-1$ |