Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 71x^{14} + 1941x^{12} + 26193x^{10} + 189059x^{8} + 736981x^{6} + 1459396x^{4} + 1193728x^{2} + 147456\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 5 | $[5, 5, -4w + 37]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 4]$ | $-e$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 17 | $[17, 17, w + 6]$ | $...$ |
| 17 | $[17, 17, w + 10]$ | $...$ |
| 19 | $[19, 19, -2w + 19]$ | $...$ |
| 19 | $[19, 19, -2w - 17]$ | $...$ |
| 23 | $[23, 23, w + 5]$ | $...$ |
| 23 | $[23, 23, w + 17]$ | $...$ |
| 37 | $[37, 37, w + 1]$ | $...$ |
| 37 | $[37, 37, w + 35]$ | $...$ |
| 41 | $[41, 41, -22w + 203]$ | $...$ |
| 41 | $[41, 41, -6w + 55]$ | $...$ |
| 43 | $[43, 43, w + 20]$ | $...$ |
| 43 | $[43, 43, w + 22]$ | $...$ |
| 53 | $[53, 53, w + 13]$ | $...$ |
| 53 | $[53, 53, w + 39]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{3586991}{156859865088}e^{15} - \frac{239222089}{156859865088}e^{13} - \frac{63856855}{1686665216}e^{11} - \frac{22942330293}{52286621696}e^{9} - \frac{392630598733}{156859865088}e^{7} - \frac{1072883097563}{156859865088}e^{5} - \frac{316740541103}{39214966272}e^{3} - \frac{559340627}{153183462}e$ |
| $2$ | $[2, 2, w + 1]$ | $\frac{3586991}{156859865088}e^{15} + \frac{239222089}{156859865088}e^{13} + \frac{63856855}{1686665216}e^{11} + \frac{22942330293}{52286621696}e^{9} + \frac{392630598733}{156859865088}e^{7} + \frac{1072883097563}{156859865088}e^{5} + \frac{316740541103}{39214966272}e^{3} + \frac{559340627}{153183462}e$ |