Base field \(\Q(\sqrt{281}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + 2x^{10} - 13x^{9} - 23x^{8} + 60x^{7} + 86x^{6} - 123x^{5} - 122x^{4} + 107x^{3} + 56x^{2} - 32x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w + 9]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -76w + 675]$ | $-\frac{1}{2}e^{9} + 6e^{7} - \frac{3}{2}e^{6} - 22e^{5} + \frac{19}{2}e^{4} + \frac{53}{2}e^{3} - \frac{21}{2}e^{2} - 9e + \frac{3}{2}$ |
| 5 | $[5, 5, 76w + 599]$ | $-\frac{1}{2}e^{9} + 6e^{7} - \frac{3}{2}e^{6} - 22e^{5} + \frac{19}{2}e^{4} + \frac{53}{2}e^{3} - \frac{21}{2}e^{2} - 9e + \frac{3}{2}$ |
| 7 | $[7, 7, -8w - 63]$ | $\phantom{-}e^{9} + e^{8} - 12e^{7} - 9e^{6} + 46e^{5} + 23e^{4} - 64e^{3} - 19e^{2} + 25e + 2$ |
| 7 | $[7, 7, -8w + 71]$ | $\phantom{-}e^{9} + e^{8} - 12e^{7} - 9e^{6} + 46e^{5} + 23e^{4} - 64e^{3} - 19e^{2} + 25e + 2$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{2}e^{9} + 7e^{7} - \frac{1}{2}e^{6} - 32e^{5} + \frac{5}{2}e^{4} + \frac{107}{2}e^{3} - \frac{3}{2}e^{2} - 26e + \frac{5}{2}$ |
| 17 | $[17, 17, 42w + 331]$ | $\phantom{-}\frac{1}{2}e^{10} - e^{9} - 7e^{8} + \frac{27}{2}e^{7} + 31e^{6} - \frac{111}{2}e^{5} - \frac{101}{2}e^{4} + \frac{149}{2}e^{3} + 34e^{2} - \frac{53}{2}e - 6$ |
| 17 | $[17, 17, 42w - 373]$ | $\phantom{-}\frac{1}{2}e^{10} - e^{9} - 7e^{8} + \frac{27}{2}e^{7} + 31e^{6} - \frac{111}{2}e^{5} - \frac{101}{2}e^{4} + \frac{149}{2}e^{3} + 34e^{2} - \frac{53}{2}e - 6$ |
| 29 | $[29, 29, -6w - 47]$ | $\phantom{-}\frac{1}{2}e^{10} - e^{9} - 7e^{8} + \frac{27}{2}e^{7} + 30e^{6} - \frac{113}{2}e^{5} - \frac{81}{2}e^{4} + \frac{163}{2}e^{3} + 9e^{2} - \frac{69}{2}e + 3$ |
| 29 | $[29, 29, 6w - 53]$ | $\phantom{-}\frac{1}{2}e^{10} - e^{9} - 7e^{8} + \frac{27}{2}e^{7} + 30e^{6} - \frac{113}{2}e^{5} - \frac{81}{2}e^{4} + \frac{163}{2}e^{3} + 9e^{2} - \frac{69}{2}e + 3$ |
| 31 | $[31, 31, 10w + 79]$ | $\phantom{-}2e^{10} + e^{9} - 25e^{8} - 7e^{7} + 100e^{6} + 11e^{5} - 144e^{4} - 8e^{3} + 59e^{2} + 3e + 2$ |
| 31 | $[31, 31, -10w + 89]$ | $\phantom{-}2e^{10} + e^{9} - 25e^{8} - 7e^{7} + 100e^{6} + 11e^{5} - 144e^{4} - 8e^{3} + 59e^{2} + 3e + 2$ |
| 43 | $[43, 43, 2w - 19]$ | $-e^{10} - e^{9} + 12e^{8} + 9e^{7} - 47e^{6} - 24e^{5} + 74e^{4} + 25e^{3} - 50e^{2} - 7e + 8$ |
| 43 | $[43, 43, -2w - 17]$ | $-e^{10} - e^{9} + 12e^{8} + 9e^{7} - 47e^{6} - 24e^{5} + 74e^{4} + 25e^{3} - 50e^{2} - 7e + 8$ |
| 53 | $[53, 53, 194w + 1529]$ | $-e^{10} - \frac{1}{2}e^{9} + 13e^{8} + 3e^{7} - \frac{113}{2}e^{6} + 2e^{5} + \frac{197}{2}e^{4} - \frac{53}{2}e^{3} - \frac{131}{2}e^{2} + 28e + \frac{21}{2}$ |
| 53 | $[53, 53, -194w + 1723]$ | $-e^{10} - \frac{1}{2}e^{9} + 13e^{8} + 3e^{7} - \frac{113}{2}e^{6} + 2e^{5} + \frac{197}{2}e^{4} - \frac{53}{2}e^{3} - \frac{131}{2}e^{2} + 28e + \frac{21}{2}$ |
| 59 | $[59, 59, -110w - 867]$ | $\phantom{-}e^{10} + 3e^{9} - 11e^{8} - 33e^{7} + 40e^{6} + 112e^{5} - 61e^{4} - 128e^{3} + 31e^{2} + 32e$ |
| 59 | $[59, 59, 110w - 977]$ | $\phantom{-}e^{10} + 3e^{9} - 11e^{8} - 33e^{7} + 40e^{6} + 112e^{5} - 61e^{4} - 128e^{3} + 31e^{2} + 32e$ |
| 79 | $[79, 79, 650w - 5773]$ | $\phantom{-}e^{10} + e^{9} - 13e^{8} - 9e^{7} + 58e^{6} + 21e^{5} - 108e^{4} - 9e^{3} + 77e^{2} - 13$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).