Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 138x^{6} + 6525x^{4} - 158436x^{2} + 4435236\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}\frac{419}{76157172}e^{7} - \frac{8467}{12692862}e^{5} + \frac{219301}{8461908}e^{3} - \frac{33959}{156702}e$ |
| 11 | $[11, 11, w + 7]$ | $-\frac{419}{76157172}e^{7} + \frac{8467}{12692862}e^{5} - \frac{219301}{8461908}e^{3} + \frac{33959}{156702}e$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{419}{76157172}e^{7} + \frac{8467}{12692862}e^{5} - \frac{219301}{8461908}e^{3} + \frac{190661}{156702}e$ |
| 23 | $[23, 23, w + 4]$ | $-\frac{8}{2115477}e^{7} - \frac{113}{705159}e^{5} + \frac{1243}{78351}e^{3} + \frac{19774}{78351}e$ |
| 23 | $[23, 23, w + 18]$ | $\phantom{-}\frac{8}{2115477}e^{7} + \frac{113}{705159}e^{5} - \frac{1243}{78351}e^{3} - \frac{19774}{78351}e$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{10}{162729}e^{6} - \frac{361}{54243}e^{4} + \frac{1868}{18081}e^{2} + \frac{7498}{2009}$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}\frac{563}{76157172}e^{7} - \frac{3725}{6346431}e^{5} + \frac{152179}{8461908}e^{3} - \frac{17911}{52234}e$ |
| 29 | $[29, 29, w + 27]$ | $-\frac{563}{76157172}e^{7} + \frac{3725}{6346431}e^{5} - \frac{152179}{8461908}e^{3} + \frac{17911}{52234}e$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{1}{31752}e^{6} + \frac{1}{1323}e^{4} - \frac{607}{3528}e^{2} + \frac{321}{196}$ |
| 31 | $[31, 31, w + 17]$ | $-\frac{1}{31752}e^{6} - \frac{1}{1323}e^{4} + \frac{607}{3528}e^{2} - \frac{321}{196}$ |
| 43 | $[43, 43, -w - 11]$ | $-\frac{10}{162729}e^{6} + \frac{361}{54243}e^{4} - \frac{1868}{18081}e^{2} + \frac{4556}{2009}$ |
| 43 | $[43, 43, w - 12]$ | $-\frac{10}{162729}e^{6} + \frac{361}{54243}e^{4} - \frac{1868}{18081}e^{2} + \frac{4556}{2009}$ |
| 47 | $[47, 47, -w - 6]$ | $-\frac{419}{76157172}e^{7} + \frac{8467}{12692862}e^{5} - \frac{219301}{8461908}e^{3} + \frac{190661}{156702}e$ |
| 47 | $[47, 47, w - 7]$ | $-\frac{419}{76157172}e^{7} + \frac{8467}{12692862}e^{5} - \frac{219301}{8461908}e^{3} + \frac{190661}{156702}e$ |
| 59 | $[59, 59, -w - 5]$ | $-\frac{2179}{304628688}e^{7} + \frac{11077}{25385724}e^{5} + \frac{862249}{33847632}e^{3} - \frac{606533}{626808}e$ |
| 59 | $[59, 59, w - 6]$ | $-\frac{2179}{304628688}e^{7} + \frac{11077}{25385724}e^{5} + \frac{862249}{33847632}e^{3} - \frac{606533}{626808}e$ |
| 61 | $[61, 61, w + 16]$ | $\phantom{-}\frac{1}{31752}e^{6} + \frac{1}{1323}e^{4} - \frac{607}{3528}e^{2} + \frac{321}{196}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |