Base field \(\Q(\sqrt{201}) \)
Generator \(w\), with minimal polynomial \(x^2 - x - 50\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} - 19 x^8 + 132 x^6 - 414 x^4 + 585 x^2 - 293\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17 w - 112]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -17 w + 129]$ | $-e$ |
| 3 | $[3, 3, -124 w + 941]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -2 w + 15]$ | $\phantom{-}\frac{1}{2} e^9 - 8 e^7 + 42 e^5 - 80 e^3 + \frac{87}{2} e$ |
| 5 | $[5, 5, -2 w - 13]$ | $-\frac{1}{2} e^9 + 8 e^7 - 42 e^5 + 80 e^3 - \frac{87}{2} e$ |
| 11 | $[11, 11, 12 w + 79]$ | $\phantom{-}2 e^9 - 33 e^7 + 181 e^5 - 370 e^3 + 228 e$ |
| 11 | $[11, 11, -12 w + 91]$ | $-2 e^9 + 33 e^7 - 181 e^5 + 370 e^3 - 228 e$ |
| 19 | $[19, 19, -90 w - 593]$ | $\phantom{-}2 e^8 - 33 e^6 + 182 e^4 - 378 e^2 + 241$ |
| 19 | $[19, 19, 90 w - 683]$ | $\phantom{-}2 e^8 - 33 e^6 + 182 e^4 - 378 e^2 + 241$ |
| 37 | $[37, 37, -4 w - 27]$ | $-\frac{3}{2} e^8 + 25 e^6 - 140 e^4 + 299 e^2 - \frac{397}{2}$ |
| 37 | $[37, 37, -4 w + 31]$ | $-\frac{3}{2} e^8 + 25 e^6 - 140 e^4 + 299 e^2 - \frac{397}{2}$ |
| 41 | $[41, 41, 158 w + 1041]$ | $\phantom{-}\frac{5}{2} e^9 - 41 e^7 + 224 e^5 - 458 e^3 + \frac{565}{2} e$ |
| 41 | $[41, 41, 158 w - 1199]$ | $-\frac{5}{2} e^9 + 41 e^7 - 224 e^5 + 458 e^3 - \frac{565}{2} e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{13}{2} e^8 - 107 e^6 + 586 e^4 - 1198 e^2 + \frac{1493}{2}$ |
| 53 | $[53, 53, 46 w - 349]$ | $\phantom{-}\frac{9}{2} e^9 - 74 e^7 + 406 e^5 - 839 e^3 + \frac{1073}{2} e$ |
| 53 | $[53, 53, 46 w + 303]$ | $-\frac{9}{2} e^9 + 74 e^7 - 406 e^5 + 839 e^3 - \frac{1073}{2} e$ |
| 67 | $[67, 67, 586 w - 4447]$ | $\phantom{-}3 e^8 - 50 e^6 + 280 e^4 - 596 e^2 + 397$ |
| 73 | $[73, 73, -32 w - 211]$ | $-\frac{19}{2} e^8 + 156 e^6 - 852 e^4 + 1739 e^2 - \frac{2155}{2}$ |
| 73 | $[73, 73, 32 w - 243]$ | $-\frac{19}{2} e^8 + 156 e^6 - 852 e^4 + 1739 e^2 - \frac{2155}{2}$ |
| 101 | $[101, 101, 2 w - 11]$ | $-e^9 + 17 e^7 - 98 e^5 + 220 e^3 - 160 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -124 w + 941]$ | $1$ |