Base field \(\Q(\sqrt{42}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 42\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w - 7]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 102x^{6} + 2445x^{4} - 21564x^{2} + 62500\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{653}{419500}e^{7} + \frac{29553}{209750}e^{5} - \frac{182967}{83900}e^{3} + \frac{1729021}{209750}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w - 7]$ | $-1$ |
| 11 | $[11, 11, w + 3]$ | $-\frac{827}{419500}e^{7} + \frac{19276}{104875}e^{5} - \frac{268403}{83900}e^{3} + \frac{2988589}{209750}e$ |
| 11 | $[11, 11, w + 8]$ | $-\frac{827}{419500}e^{7} + \frac{19276}{104875}e^{5} - \frac{268403}{83900}e^{3} + \frac{2988589}{209750}e$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{653}{419500}e^{7} + \frac{29553}{209750}e^{5} - \frac{182967}{83900}e^{3} + \frac{1519271}{209750}e$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{653}{419500}e^{7} - \frac{29553}{209750}e^{5} + \frac{182967}{83900}e^{3} - \frac{1519271}{209750}e$ |
| 17 | $[17, 17, -w - 5]$ | $-\frac{7}{6712}e^{6} + \frac{111}{839}e^{4} - \frac{30079}{6712}e^{2} + \frac{101967}{3356}$ |
| 17 | $[17, 17, -w + 5]$ | $\phantom{-}\frac{7}{6712}e^{6} - \frac{111}{839}e^{4} + \frac{30079}{6712}e^{2} - \frac{101967}{3356}$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}\frac{5827}{839000}e^{7} - \frac{132901}{209750}e^{5} + \frac{1712803}{167800}e^{3} - \frac{18200839}{419500}e$ |
| 19 | $[19, 19, w + 17]$ | $-\frac{5827}{839000}e^{7} + \frac{132901}{209750}e^{5} - \frac{1712803}{167800}e^{3} + \frac{18200839}{419500}e$ |
| 25 | $[25, 5, 5]$ | $-\frac{20}{839}e^{6} + \frac{1818}{839}e^{4} - \frac{28888}{839}e^{2} + \frac{116664}{839}$ |
| 29 | $[29, 29, w + 10]$ | $-\frac{87}{104875}e^{7} + \frac{8999}{104875}e^{5} - \frac{42718}{20975}e^{3} + \frac{1259568}{104875}e$ |
| 29 | $[29, 29, w + 19]$ | $-\frac{87}{104875}e^{7} + \frac{8999}{104875}e^{5} - \frac{42718}{20975}e^{3} + \frac{1259568}{104875}e$ |
| 41 | $[41, 41, -w - 1]$ | $-\frac{131}{6712}e^{6} + \frac{1478}{839}e^{4} - \frac{180323}{6712}e^{2} + \frac{334755}{3356}$ |
| 41 | $[41, 41, w - 1]$ | $\phantom{-}\frac{131}{6712}e^{6} - \frac{1478}{839}e^{4} + \frac{180323}{6712}e^{2} - \frac{334755}{3356}$ |
| 47 | $[47, 47, -2w + 11]$ | $\phantom{-}0$ |
| 47 | $[47, 47, 4w - 25]$ | $\phantom{-}0$ |
| 53 | $[53, 53, w + 25]$ | $-\frac{566}{104875}e^{7} + \frac{50107}{104875}e^{5} - \frac{140249}{20975}e^{3} + \frac{2198474}{104875}e$ |
| 53 | $[53, 53, w + 28]$ | $-\frac{566}{104875}e^{7} + \frac{50107}{104875}e^{5} - \frac{140249}{20975}e^{3} + \frac{2198474}{104875}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w - 7]$ | $1$ |