Base field \(\Q(\sqrt{46}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[14, 14, -3w - 20]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} + x^{6} - 14x^{5} - 16x^{4} + 51x^{3} + 62x^{2} - 52x - 65\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, 23w - 156]$ | $\phantom{-}1$ |
3 | $[3, 3, -w - 7]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 7]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{1}{2}e^{5} - 3e^{4} + 5e^{3} + \frac{35}{4}e^{2} - \frac{35}{4}e - \frac{31}{4}$ |
5 | $[5, 5, -9w + 61]$ | $\phantom{-}\frac{3}{4}e^{6} - \frac{1}{2}e^{5} - 10e^{4} + 4e^{3} + \frac{141}{4}e^{2} - \frac{21}{4}e - \frac{149}{4}$ |
5 | $[5, 5, -9w - 61]$ | $-\frac{1}{4}e^{6} + \frac{1}{2}e^{5} + 3e^{4} - 5e^{3} - \frac{35}{4}e^{2} + \frac{35}{4}e + \frac{23}{4}$ |
7 | $[7, 7, 4w - 27]$ | $-1$ |
7 | $[7, 7, 4w + 27]$ | $-2e^{6} + e^{5} + 27e^{4} - 8e^{3} - 96e^{2} + 13e + 98$ |
23 | $[23, 23, 78w - 529]$ | $-\frac{3}{4}e^{6} + \frac{1}{2}e^{5} + 10e^{4} - 4e^{3} - \frac{137}{4}e^{2} + \frac{17}{4}e + \frac{129}{4}$ |
37 | $[37, 37, -w - 3]$ | $\phantom{-}5e^{6} - 3e^{5} - 66e^{4} + 25e^{3} + 225e^{2} - 41e - 221$ |
37 | $[37, 37, w - 3]$ | $-\frac{5}{4}e^{6} + \frac{1}{2}e^{5} + 18e^{4} - 4e^{3} - \frac{287}{4}e^{2} + \frac{19}{4}e + \frac{319}{4}$ |
41 | $[41, 41, -2w + 15]$ | $\phantom{-}\frac{21}{4}e^{6} - \frac{7}{2}e^{5} - 69e^{4} + 30e^{3} + \frac{931}{4}e^{2} - \frac{191}{4}e - \frac{875}{4}$ |
41 | $[41, 41, 2w + 15]$ | $\phantom{-}\frac{3}{2}e^{6} - 19e^{4} - 3e^{3} + \frac{113}{2}e^{2} + \frac{17}{2}e - \frac{83}{2}$ |
53 | $[53, 53, -3w - 19]$ | $-\frac{5}{4}e^{6} + \frac{1}{2}e^{5} + 18e^{4} - 4e^{3} - \frac{295}{4}e^{2} + \frac{27}{4}e + \frac{351}{4}$ |
53 | $[53, 53, 3w - 19]$ | $\phantom{-}\frac{21}{4}e^{6} - \frac{5}{2}e^{5} - 70e^{4} + 18e^{3} + \frac{967}{4}e^{2} - \frac{79}{4}e - \frac{951}{4}$ |
59 | $[59, 59, 11w - 75]$ | $-\frac{5}{4}e^{6} + \frac{1}{2}e^{5} + 17e^{4} - 3e^{3} - \frac{239}{4}e^{2} - \frac{5}{4}e + \frac{215}{4}$ |
59 | $[59, 59, -11w - 75]$ | $\phantom{-}\frac{39}{4}e^{6} - \frac{9}{2}e^{5} - 129e^{4} + 33e^{3} + \frac{1749}{4}e^{2} - \frac{177}{4}e - \frac{1669}{4}$ |
61 | $[61, 61, -5w + 33]$ | $\phantom{-}e^{6} - 15e^{4} - e^{3} + 63e^{2} - 78$ |
61 | $[61, 61, 5w + 33]$ | $-\frac{15}{2}e^{6} + 3e^{5} + 100e^{4} - 20e^{3} - \frac{687}{2}e^{2} + \frac{45}{2}e + \frac{657}{2}$ |
73 | $[73, 73, -24w - 163]$ | $-\frac{17}{2}e^{6} + 5e^{5} + 110e^{4} - 41e^{3} - \frac{717}{2}e^{2} + \frac{129}{2}e + \frac{665}{2}$ |
73 | $[73, 73, -24w + 163]$ | $\phantom{-}\frac{23}{4}e^{6} - \frac{5}{2}e^{5} - 78e^{4} + 19e^{3} + \frac{1117}{4}e^{2} - \frac{105}{4}e - \frac{1141}{4}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, 23w - 156]$ | $-1$ |
$7$ | $[7, 7, 4w - 27]$ | $1$ |