Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w + 1]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 64x^{14} + 1382x^{12} + 13302x^{10} + 61327x^{8} + 139374x^{6} + 151891x^{4} + 70810x^{2} + 11449\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{567923}{731131000}e^{15} - \frac{36276559}{731131000}e^{13} - \frac{780070957}{731131000}e^{11} - \frac{7439499479}{731131000}e^{9} - \frac{4192562209}{91391375}e^{7} - \frac{7191041267}{73113100}e^{5} - \frac{66406572523}{731131000}e^{3} - \frac{17753812617}{731131000}e$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 5 | $[5, 5, -3w + 25]$ | $...$ |
| 7 | $[7, 7, w]$ | $...$ |
| 11 | $[11, 11, w - 9]$ | $-\frac{2714356}{792115525}e^{14} - \frac{34308788}{158423105}e^{12} - \frac{3615072088}{792115525}e^{10} - \frac{33287207127}{792115525}e^{8} - \frac{141291424936}{792115525}e^{6} - \frac{277006730366}{792115525}e^{4} - \frac{45741081764}{158423105}e^{2} - \frac{55449555267}{792115525}$ |
| 11 | $[11, 11, -w - 9]$ | $...$ |
| 17 | $[17, 17, w + 6]$ | $...$ |
| 17 | $[17, 17, w + 11]$ | $...$ |
| 23 | $[23, 23, w + 1]$ | $...$ |
| 23 | $[23, 23, w + 22]$ | $...$ |
| 31 | $[31, 31, 4w - 33]$ | $...$ |
| 31 | $[31, 31, 4w + 33]$ | $...$ |
| 37 | $[37, 37, w + 12]$ | $...$ |
| 37 | $[37, 37, w + 25]$ | $...$ |
| 53 | $[53, 53, w + 21]$ | $...$ |
| 53 | $[53, 53, w + 32]$ | $...$ |
| 61 | $[61, 61, -w - 3]$ | $...$ |
| 61 | $[61, 61, w - 3]$ | $...$ |
| 73 | $[73, 73, w + 17]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $\frac{567923}{731131000}e^{15} + \frac{36276559}{731131000}e^{13} + \frac{780070957}{731131000}e^{11} + \frac{7439499479}{731131000}e^{9} + \frac{4192562209}{91391375}e^{7} + \frac{7191041267}{73113100}e^{5} + \frac{66406572523}{731131000}e^{3} + \frac{17753812617}{731131000}e$ |