Base field \(\Q(\sqrt{449}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 112\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5,5,116w - 1287]$ |
| Dimension: | $39$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $101$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{39} + x^{38} - 60x^{37} - 48x^{36} + 1658x^{35} + 997x^{34} - 27936x^{33} - 11386x^{32} + 320243x^{31} + 71055x^{30} - 2638979x^{29} - 123333x^{28} + 16105821x^{27} - 1870028x^{26} - 73924766x^{25} + 19642801x^{24} + 256611526x^{23} - 103154429x^{22} - 672203067x^{21} + 353430137x^{20} + 1316438633x^{19} - 841394715x^{18} - 1894330295x^{17} + 1413225260x^{16} + 1947554274x^{15} - 1663359458x^{14} - 1366391206x^{13} + 1339237379x^{12} + 601523656x^{11} - 705016654x^{10} - 135445282x^{9} + 223939319x^{8} + 2679852x^{7} - 36734805x^{6} + 4099413x^{5} + 2142468x^{4} - 387860x^{3} - 16232x^{2} + 5262x - 201\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 10]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 11]$ | $...$ |
| 5 | $[5, 5, -116w - 1171]$ | $...$ |
| 5 | $[5, 5, 116w - 1287]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -1002w - 10115]$ | $...$ |
| 7 | $[7, 7, 1002w - 11117]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, 10w - 111]$ | $...$ |
| 11 | $[11, 11, -10w - 101]$ | $...$ |
| 23 | $[23, 23, -32w + 355]$ | $...$ |
| 23 | $[23, 23, 32w + 323]$ | $...$ |
| 41 | $[41, 41, -8w - 81]$ | $...$ |
| 41 | $[41, 41, -8w + 89]$ | $...$ |
| 53 | $[53, 53, 4w - 45]$ | $...$ |
| 53 | $[53, 53, 4w + 41]$ | $...$ |
| 59 | $[59, 59, -3892w + 43181]$ | $...$ |
| 59 | $[59, 59, 3892w + 39289]$ | $...$ |
| 61 | $[61, 61, 770w - 8543]$ | $...$ |
| 61 | $[61, 61, -770w - 7773]$ | $...$ |
| 67 | $[67, 67, 158w + 1595]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,116w - 1287]$ | $-1$ |