Base field \(\Q(\sqrt{87}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 87\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 72x^{10} + 1800x^{8} - 17280x^{6} + 42128x^{4} - 15744x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{1024}e^{11} + \frac{9}{128}e^{9} - \frac{451}{256}e^{7} + \frac{273}{16}e^{5} - \frac{697}{16}e^{3} + 20e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{1024}e^{11} - \frac{9}{128}e^{9} + \frac{451}{256}e^{7} - \frac{273}{16}e^{5} + \frac{697}{16}e^{3} - 19e$ |
| 13 | $[13, 13, -w + 10]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w + 10]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w + 6]$ | $-\frac{1}{1024}e^{11} + \frac{37}{512}e^{9} - \frac{471}{256}e^{7} + \frac{2251}{128}e^{5} - \frac{599}{16}e^{3} + \frac{25}{8}e$ |
| 17 | $[17, 17, w + 11]$ | $-\frac{1}{1024}e^{11} + \frac{37}{512}e^{9} - \frac{471}{256}e^{7} + \frac{2251}{128}e^{5} - \frac{599}{16}e^{3} + \frac{25}{8}e$ |
| 19 | $[19, 19, w + 7]$ | $-\frac{3}{1024}e^{11} + \frac{107}{512}e^{9} - \frac{1325}{256}e^{7} + \frac{6293}{128}e^{5} - \frac{1879}{16}e^{3} + \frac{327}{8}e$ |
| 19 | $[19, 19, w + 12]$ | $-\frac{3}{1024}e^{11} + \frac{107}{512}e^{9} - \frac{1325}{256}e^{7} + \frac{6293}{128}e^{5} - \frac{1879}{16}e^{3} + \frac{327}{8}e$ |
| 23 | $[23, 23, -w - 8]$ | $\phantom{-}\frac{1}{512}e^{10} - \frac{15}{128}e^{8} + \frac{303}{128}e^{6} - \frac{567}{32}e^{4} + 34e^{2} - 3$ |
| 23 | $[23, 23, w - 8]$ | $\phantom{-}\frac{1}{512}e^{10} - \frac{15}{128}e^{8} + \frac{303}{128}e^{6} - \frac{567}{32}e^{4} + 34e^{2} - 3$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{64}e^{8} - \frac{3}{4}e^{6} + \frac{159}{16}e^{4} - \frac{45}{2}e^{2} + 7$ |
| 29 | $[29, 29, w]$ | $\phantom{-}\frac{3}{512}e^{11} - \frac{109}{256}e^{9} + \frac{1373}{128}e^{7} - \frac{6619}{64}e^{5} + \frac{1993}{8}e^{3} - \frac{345}{4}e$ |
| 31 | $[31, 31, w + 5]$ | $-\frac{3}{1024}e^{11} + \frac{53}{256}e^{9} - \frac{1301}{256}e^{7} + \frac{3069}{64}e^{5} - \frac{921}{8}e^{3} + 35e$ |
| 31 | $[31, 31, w + 26]$ | $-\frac{3}{1024}e^{11} + \frac{53}{256}e^{9} - \frac{1301}{256}e^{7} + \frac{3069}{64}e^{5} - \frac{921}{8}e^{3} + 35e$ |
| 41 | $[41, 41, w + 13]$ | $\phantom{-}\frac{5}{1024}e^{11} - \frac{183}{512}e^{9} + \frac{2319}{256}e^{7} - \frac{11209}{128}e^{5} + \frac{1659}{8}e^{3} - \frac{481}{8}e$ |
| 41 | $[41, 41, w + 28]$ | $\phantom{-}\frac{5}{1024}e^{11} - \frac{183}{512}e^{9} + \frac{2319}{256}e^{7} - \frac{11209}{128}e^{5} + \frac{1659}{8}e^{3} - \frac{481}{8}e$ |
| 43 | $[43, 43, w + 1]$ | $\phantom{-}\frac{1}{256}e^{11} - \frac{141}{512}e^{9} + \frac{431}{64}e^{7} - \frac{8063}{128}e^{5} + \frac{2327}{16}e^{3} - \frac{303}{8}e$ |
| 43 | $[43, 43, w + 42]$ | $\phantom{-}\frac{1}{256}e^{11} - \frac{141}{512}e^{9} + \frac{431}{64}e^{7} - \frac{8063}{128}e^{5} + \frac{2327}{16}e^{3} - \frac{303}{8}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{128}e^{8} - \frac{3}{8}e^{6} + \frac{163}{32}e^{4} - \frac{57}{4}e^{2} + \frac{25}{2}$ |
| 59 | $[59, 59, -2w + 17]$ | $-\frac{1}{512}e^{10} + \frac{15}{128}e^{8} - \frac{307}{128}e^{6} + \frac{603}{32}e^{4} - \frac{351}{8}e^{2} + \frac{27}{2}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).