Base field 5.5.70601.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[53, 53, -w^{4} + 7w^{2} - 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 5x^{6} - 18x^{5} - 80x^{4} + 108x^{3} + 252x^{2} - 324x + 81\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 6w^{2} - 2w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - w - 4]$ | $\phantom{-}\frac{140}{5913}e^{6} + \frac{985}{5913}e^{5} - \frac{242}{1971}e^{4} - \frac{13945}{5913}e^{3} - \frac{3226}{1971}e^{2} + \frac{3655}{657}e + \frac{151}{219}$ |
| 11 | $[11, 11, -2w^{4} + w^{3} + 10w^{2} + w - 3]$ | $\phantom{-}\frac{1}{657}e^{6} - \frac{2}{219}e^{5} - \frac{25}{657}e^{4} + \frac{268}{657}e^{3} + \frac{7}{657}e^{2} - \frac{842}{219}e + \frac{34}{73}$ |
| 11 | $[11, 11, w^{4} - 6w^{2} - 3w + 3]$ | $\phantom{-}\frac{112}{5913}e^{6} + \frac{788}{5913}e^{5} - \frac{325}{1971}e^{4} - \frac{13127}{5913}e^{3} - \frac{1004}{1971}e^{2} + \frac{5114}{657}e - \frac{799}{219}$ |
| 17 | $[17, 17, w^{2} - 2]$ | $-\frac{607}{5913}e^{6} - \frac{3731}{5913}e^{5} + \frac{2479}{1971}e^{4} + \frac{57857}{5913}e^{3} - \frac{6064}{1971}e^{2} - \frac{19265}{657}e + \frac{3073}{219}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w]$ | $\phantom{-}\frac{230}{1971}e^{6} + \frac{1321}{1971}e^{5} - \frac{355}{219}e^{4} - \frac{20704}{1971}e^{3} + \frac{1282}{219}e^{2} + \frac{2410}{73}e - \frac{1530}{73}$ |
| 27 | $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ | $-\frac{149}{5913}e^{6} - \frac{931}{5913}e^{5} + \frac{317}{1971}e^{4} + \frac{11533}{5913}e^{3} + \frac{3205}{1971}e^{2} - \frac{1129}{657}e - \frac{1348}{219}$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ | $-\frac{794}{5913}e^{6} - \frac{4507}{5913}e^{5} + \frac{3575}{1971}e^{4} + \frac{69937}{5913}e^{3} - \frac{9980}{1971}e^{2} - \frac{23842}{657}e + \frac{3752}{219}$ |
| 32 | $[32, 2, -2]$ | $\phantom{-}\frac{257}{5913}e^{6} + \frac{1597}{5913}e^{5} - \frac{998}{1971}e^{4} - \frac{23980}{5913}e^{3} + \frac{1427}{1971}e^{2} + \frac{6295}{657}e - \frac{1151}{219}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{911}{5913}e^{6} + \frac{5119}{5913}e^{5} - \frac{4331}{1971}e^{4} - \frac{79972}{5913}e^{3} + \frac{14633}{1971}e^{2} + \frac{27139}{657}e - \frac{4616}{219}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $-\frac{151}{1971}e^{6} - \frac{992}{1971}e^{5} + \frac{577}{657}e^{4} + \frac{16472}{1971}e^{3} - \frac{547}{657}e^{2} - \frac{2071}{73}e + \frac{430}{73}$ |
| 53 | $[53, 53, -w^{4} + 7w^{2} - 3]$ | $-1$ |
| 53 | $[53, 53, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 2]$ | $\phantom{-}\frac{541}{5913}e^{6} + \frac{3032}{5913}e^{5} - \frac{2878}{1971}e^{4} - \frac{50579}{5913}e^{3} + \frac{14743}{1971}e^{2} + \frac{19904}{657}e - \frac{4843}{219}$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 16w^{2} + 8]$ | $-\frac{137}{1971}e^{6} - \frac{1003}{1971}e^{5} + \frac{217}{657}e^{4} + \frac{14749}{1971}e^{3} + \frac{3233}{657}e^{2} - \frac{1572}{73}e + \frac{29}{73}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 4w - 3]$ | $-\frac{35}{219}e^{6} - \frac{538}{657}e^{5} + \frac{1603}{657}e^{4} + \frac{864}{73}e^{3} - \frac{6502}{657}e^{2} - \frac{6782}{219}e + \frac{1467}{73}$ |
| 73 | $[73, 73, 2w^{4} - 12w^{2} - 4w + 5]$ | $\phantom{-}\frac{742}{5913}e^{6} + \frac{3578}{5913}e^{5} - \frac{4480}{1971}e^{4} - \frac{57155}{5913}e^{3} + \frac{22366}{1971}e^{2} + \frac{19481}{657}e - \frac{4609}{219}$ |
| 83 | $[83, 83, w^{4} - 5w^{2} - 3w + 3]$ | $-\frac{310}{1971}e^{6} - \frac{1571}{1971}e^{5} + \frac{1756}{657}e^{4} + \frac{25763}{1971}e^{3} - \frac{7999}{657}e^{2} - \frac{3207}{73}e + \frac{1986}{73}$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-\frac{268}{5913}e^{6} - \frac{947}{5913}e^{5} + \frac{1990}{1971}e^{4} + \frac{15995}{5913}e^{3} - \frac{8266}{1971}e^{2} - \frac{5057}{657}e - \frac{1334}{219}$ |
| 103 | $[103, 103, 2w^{3} - 3w^{2} - 7w + 3]$ | $-\frac{763}{5913}e^{6} - \frac{4547}{5913}e^{5} + \frac{3706}{1971}e^{4} + \frac{76493}{5913}e^{3} - \frac{15553}{1971}e^{2} - \frac{32786}{657}e + \frac{5320}{219}$ |
| 109 | $[109, 109, -3w^{4} + 2w^{3} + 14w^{2} + w - 6]$ | $-\frac{1280}{5913}e^{6} - \frac{6847}{5913}e^{5} + \frac{6092}{1971}e^{4} + \frac{101311}{5913}e^{3} - \frac{20750}{1971}e^{2} - \frac{30883}{657}e + \frac{5471}{219}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53, 53, -w^{4} + 7w^{2} - 3]$ | $1$ |