Base field 4.4.7053.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, -2w^{3} + 5w^{2} + 4w - 7]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - x^{9} - 19x^{8} + 16x^{7} + 106x^{6} - 41x^{5} - 220x^{4} - 31x^{3} + 92x^{2} + 42x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - w - 2]$ | $-\frac{4}{5}e^{9} + 3e^{8} + \frac{46}{5}e^{7} - \frac{223}{5}e^{6} + \frac{33}{5}e^{5} + \frac{567}{5}e^{4} - \frac{363}{5}e^{3} - \frac{214}{5}e^{2} + \frac{143}{5}e + 7$ |
| 9 | $[9, 3, w^{2} - 2w - 1]$ | $\phantom{-}\frac{13}{5}e^{9} - 5e^{8} - \frac{217}{5}e^{7} + \frac{391}{5}e^{6} + \frac{919}{5}e^{5} - \frac{1119}{5}e^{4} - \frac{1604}{5}e^{3} + \frac{388}{5}e^{2} + \frac{749}{5}e + 31$ |
| 13 | $[13, 13, w^{3} - 3w^{2} - w + 5]$ | $\phantom{-}e^{9} - 2e^{8} - 17e^{7} + 32e^{6} + 75e^{5} - 101e^{4} - 134e^{3} + 58e^{2} + 59e + 6$ |
| 13 | $[13, 13, w^{3} - 3w^{2} - w + 2]$ | $-5e^{9} + 7e^{8} + 92e^{7} - 116e^{6} - 481e^{5} + 385e^{4} + 943e^{3} - 185e^{2} - 388e - 76$ |
| 16 | $[16, 2, 2]$ | $-\frac{28}{5}e^{9} + 8e^{8} + \frac{512}{5}e^{7} - \frac{661}{5}e^{6} - \frac{2644}{5}e^{5} + \frac{2184}{5}e^{4} + \frac{5129}{5}e^{3} - \frac{1083}{5}e^{2} - \frac{2079}{5}e - 77$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 2w - 2]$ | $-4e^{9} + 7e^{8} + 69e^{7} - 111e^{6} - 316e^{5} + 329e^{4} + 577e^{3} - 118e^{2} - 249e - 52$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 2w - 1]$ | $\phantom{-}\frac{16}{5}e^{9} - 4e^{8} - \frac{299}{5}e^{7} + \frac{332}{5}e^{6} + \frac{1613}{5}e^{5} - \frac{1078}{5}e^{4} - \frac{3248}{5}e^{3} + \frac{376}{5}e^{2} + \frac{1383}{5}e + 58$ |
| 29 | $[29, 29, -2w^{3} + 5w^{2} + 4w - 7]$ | $-1$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}\frac{19}{5}e^{9} - 9e^{8} - \frac{296}{5}e^{7} + \frac{698}{5}e^{6} + \frac{1017}{5}e^{5} - \frac{2007}{5}e^{4} - \frac{1422}{5}e^{3} + \frac{959}{5}e^{2} + \frac{627}{5}e + 8$ |
| 47 | $[47, 47, -w^{3} + 4w^{2} - w - 5]$ | $\phantom{-}\frac{4}{5}e^{9} - 7e^{8} + \frac{19}{5}e^{7} + \frac{483}{5}e^{6} - \frac{1003}{5}e^{5} - \frac{867}{5}e^{4} + \frac{2828}{5}e^{3} - \frac{226}{5}e^{2} - \frac{893}{5}e - 19$ |
| 53 | $[53, 53, -w^{3} + 4w^{2} - w - 7]$ | $\phantom{-}\frac{2}{5}e^{9} + 3e^{8} - \frac{88}{5}e^{7} - \frac{201}{5}e^{6} + \frac{966}{5}e^{5} + \frac{349}{5}e^{4} - \frac{2426}{5}e^{3} - \frac{68}{5}e^{2} + \frac{956}{5}e + 41$ |
| 67 | $[67, 67, 2w^{3} - 3w^{2} - 8w + 1]$ | $-\frac{2}{5}e^{9} - e^{8} + \frac{63}{5}e^{7} + \frac{46}{5}e^{6} - \frac{576}{5}e^{5} + \frac{171}{5}e^{4} + \frac{1261}{5}e^{3} - \frac{617}{5}e^{2} - \frac{261}{5}e + 12$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 4w + 4]$ | $-\frac{39}{5}e^{9} + 12e^{8} + \frac{706}{5}e^{7} - \frac{993}{5}e^{6} - \frac{3567}{5}e^{5} + \frac{3352}{5}e^{4} + \frac{6772}{5}e^{3} - \frac{1989}{5}e^{2} - \frac{2627}{5}e - 77$ |
| 71 | $[71, 71, w^{3} - 3w^{2} - 2w + 2]$ | $\phantom{-}6e^{9} - 4e^{8} - 123e^{7} + 77e^{6} + 768e^{5} - 322e^{4} - 1641e^{3} + 141e^{2} + 654e + 139$ |
| 79 | $[79, 79, w^{2} - 3w - 4]$ | $-\frac{49}{5}e^{9} + 13e^{8} + \frac{911}{5}e^{7} - \frac{1083}{5}e^{6} - \frac{4857}{5}e^{5} + \frac{3617}{5}e^{4} + \frac{9632}{5}e^{3} - \frac{1654}{5}e^{2} - \frac{3952}{5}e - 155$ |
| 83 | $[83, 83, 2w^{2} - 3w - 4]$ | $\phantom{-}\frac{49}{5}e^{9} - 22e^{8} - \frac{781}{5}e^{7} + \frac{1713}{5}e^{6} + \frac{2892}{5}e^{5} - \frac{4962}{5}e^{4} - \frac{4417}{5}e^{3} + \frac{2299}{5}e^{2} + \frac{1987}{5}e + 45$ |
| 89 | $[89, 89, -3w^{3} + 7w^{2} + 8w - 11]$ | $\phantom{-}\frac{33}{5}e^{9} - 11e^{8} - \frac{582}{5}e^{7} + \frac{891}{5}e^{6} + \frac{2789}{5}e^{5} - \frac{2839}{5}e^{4} - \frac{5149}{5}e^{3} + \frac{1458}{5}e^{2} + \frac{2054}{5}e + 64$ |
| 101 | $[101, 101, w^{3} - 2w^{2} - 3w - 2]$ | $\phantom{-}\frac{63}{5}e^{9} - 27e^{8} - \frac{1022}{5}e^{7} + \frac{2111}{5}e^{6} + \frac{3989}{5}e^{5} - \frac{6164}{5}e^{4} - \frac{6399}{5}e^{3} + \frac{2793}{5}e^{2} + \frac{2824}{5}e + 83$ |
| 103 | $[103, 103, -2w^{3} + 4w^{2} + 5w - 1]$ | $\phantom{-}\frac{87}{5}e^{9} - 36e^{8} - \frac{1423}{5}e^{7} + \frac{2804}{5}e^{6} + \frac{5696}{5}e^{5} - \frac{8006}{5}e^{4} - \frac{9431}{5}e^{3} + \frac{2992}{5}e^{2} + \frac{4236}{5}e + 164$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -2w^{3} + 5w^{2} + 4w - 7]$ | $1$ |