Base field 4.4.18688.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[28, 14, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - 4w + \frac{28}{3}]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 4x^{9} - 34x^{8} + 139x^{7} + 352x^{6} - 1461x^{5} - 1422x^{4} + 5424x^{3} + 3280x^{2} - 6656x - 4096\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
7 | $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ | $\phantom{-}1$ |
7 | $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ | $\phantom{-}e$ |
9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ | $...$ |
9 | $[9, 3, w + 1]$ | $...$ |
17 | $[17, 17, w + 3]$ | $...$ |
17 | $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ | $...$ |
31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ | $-\frac{99175}{7791248}e^{9} + \frac{21609}{486953}e^{8} + \frac{1593891}{3895624}e^{7} - \frac{11167717}{7791248}e^{6} - \frac{7090681}{1947812}e^{5} + \frac{99289755}{7791248}e^{4} + \frac{33730791}{3895624}e^{3} - \frac{15144010}{486953}e^{2} - \frac{1611541}{486953}e + \frac{8196024}{486953}$ |
31 | $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ | $...$ |
41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ | $...$ |
41 | $[41, 41, w^{2} - 5]$ | $...$ |
41 | $[41, 41, 2w + 3]$ | $-\frac{54747}{31164992}e^{9} + \frac{12171}{7791248}e^{8} + \frac{754739}{15582496}e^{7} - \frac{1781129}{31164992}e^{6} - \frac{145512}{486953}e^{5} + \frac{18017863}{31164992}e^{4} - \frac{723539}{15582496}e^{3} - \frac{2777525}{973906}e^{2} + \frac{498625}{1947812}e + \frac{3389625}{486953}$ |
41 | $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ | $...$ |
47 | $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ | $-\frac{8129}{3895624}e^{9} + \frac{72005}{1947812}e^{8} - \frac{82637}{1947812}e^{7} - \frac{4732655}{3895624}e^{6} + \frac{5505149}{1947812}e^{5} + \frac{44285417}{3895624}e^{4} - \frac{13143158}{486953}e^{3} - \frac{16026271}{486953}e^{2} + \frac{26218601}{486953}e + \frac{17446240}{486953}$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ | $...$ |
49 | $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ | $...$ |
73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ | $...$ |
73 | $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ | $...$ |
73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ | $\phantom{-}\frac{11463}{1947812}e^{9} - \frac{21027}{973906}e^{8} - \frac{86072}{486953}e^{7} + \frac{1236637}{1947812}e^{6} + \frac{1340715}{973906}e^{5} - \frac{8295885}{1947812}e^{4} - \frac{1394624}{486953}e^{3} - \frac{175797}{973906}e^{2} + \frac{2423842}{486953}e + \frac{8236686}{486953}$ |
103 | $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 2]$ | $-1$ |
$7$ | $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ | $-1$ |