Base field 5.5.81589.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[43, 43, -w^{3} + 4w - 2]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 6x^{13} - 2x^{12} + 69x^{11} - 65x^{10} - 286x^{9} + 403x^{8} + 518x^{7} - 911x^{6} - 344x^{5} + 862x^{4} - 50x^{3} - 262x^{2} + 87x - 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} - 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{4} + 5w^{2} + w - 4]$ | $-\frac{5}{4}e^{13} + \frac{35}{4}e^{12} - \frac{29}{4}e^{11} - 72e^{10} + \frac{589}{4}e^{9} + \frac{613}{4}e^{8} - 538e^{7} + \frac{17}{2}e^{6} + \frac{2805}{4}e^{5} - \frac{1021}{4}e^{4} - \frac{1117}{4}e^{3} + \frac{531}{4}e^{2} - \frac{9}{4}e - \frac{3}{2}$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{3}{4}e^{13} + \frac{17}{4}e^{12} + \frac{9}{4}e^{11} - 47e^{10} + \frac{131}{4}e^{9} + \frac{755}{4}e^{8} - 194e^{7} - \frac{699}{2}e^{6} + \frac{1527}{4}e^{5} + \frac{1185}{4}e^{4} - \frac{1191}{4}e^{3} - \frac{355}{4}e^{2} + \frac{281}{4}e - \frac{3}{2}$ |
| 16 | $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{4}e^{13} - \frac{3}{4}e^{12} - \frac{19}{4}e^{11} + 16e^{10} + \frac{103}{4}e^{9} - \frac{433}{4}e^{8} - 39e^{7} + \frac{601}{2}e^{6} - \frac{145}{4}e^{5} - \frac{1367}{4}e^{4} + \frac{457}{4}e^{3} + \frac{461}{4}e^{2} - \frac{195}{4}e + \frac{11}{2}$ |
| 17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $\phantom{-}\frac{1}{2}e^{13} - \frac{7}{2}e^{12} + \frac{9}{2}e^{11} + 20e^{10} - \frac{123}{2}e^{9} + \frac{41}{2}e^{8} + 145e^{7} - 248e^{6} + \frac{25}{2}e^{5} + \frac{755}{2}e^{4} - \frac{509}{2}e^{3} - \frac{267}{2}e^{2} + \frac{247}{2}e - 17$ |
| 31 | $[31, 31, w^{4} - 4w^{2} - w + 3]$ | $\phantom{-}2e^{12} - 12e^{11} + 2e^{10} + 105e^{9} - 138e^{8} - 271e^{7} + 524e^{6} + 181e^{5} - 649e^{4} + 121e^{3} + 217e^{2} - 106e + 12$ |
| 43 | $[43, 43, -w^{3} + 4w - 2]$ | $\phantom{-}1$ |
| 53 | $[53, 53, w^{4} - 3w^{2} - 1]$ | $-\frac{1}{4}e^{13} - \frac{5}{4}e^{12} + \frac{75}{4}e^{11} - 29e^{10} - \frac{539}{4}e^{9} + \frac{1405}{4}e^{8} + 227e^{7} - \frac{2307}{2}e^{6} + \frac{873}{4}e^{5} + \frac{5567}{4}e^{4} - \frac{2833}{4}e^{3} - \frac{1881}{4}e^{2} + \frac{1283}{4}e - \frac{79}{2}$ |
| 53 | $[53, 53, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-\frac{5}{4}e^{13} + \frac{35}{4}e^{12} - \frac{29}{4}e^{11} - 73e^{10} + \frac{601}{4}e^{9} + \frac{661}{4}e^{8} - 572e^{7} - \frac{91}{2}e^{6} + \frac{3313}{4}e^{5} - \frac{581}{4}e^{4} - \frac{1793}{4}e^{3} + \frac{215}{4}e^{2} + \frac{223}{4}e - \frac{5}{2}$ |
| 53 | $[53, 53, -w^{3} - w^{2} + 3w + 4]$ | $-\frac{1}{2}e^{13} + \frac{9}{2}e^{12} - \frac{21}{2}e^{11} - 19e^{10} + \frac{231}{2}e^{9} - \frac{189}{2}e^{8} - 292e^{7} + 553e^{6} + \frac{207}{2}e^{5} - \frac{1625}{2}e^{4} + \frac{583}{2}e^{3} + \frac{671}{2}e^{2} - \frac{327}{2}e + 7$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}\frac{15}{4}e^{13} - \frac{101}{4}e^{12} + \frac{63}{4}e^{11} + 216e^{10} - \frac{1539}{4}e^{9} - \frac{2099}{4}e^{8} + 1439e^{7} + \frac{511}{2}e^{6} - \frac{7631}{4}e^{5} + \frac{1387}{4}e^{4} + \frac{3203}{4}e^{3} - \frac{753}{4}e^{2} - \frac{93}{4}e - \frac{9}{2}$ |
| 61 | $[61, 61, w^{4} - 4w^{2} + w + 1]$ | $-2e^{13} + 16e^{12} - 25e^{11} - 105e^{10} + 342e^{9} + 29e^{8} - 1062e^{7} + 784e^{6} + 1025e^{5} - 1367e^{4} - 3e^{3} + 554e^{2} - 192e + 18$ |
| 61 | $[61, 61, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}3e^{13} - 21e^{12} + 17e^{11} + 175e^{10} - 353e^{9} - 388e^{8} + 1312e^{7} + 38e^{6} - 1769e^{5} + 554e^{4} + 777e^{3} - 316e^{2} - 32e + 15$ |
| 67 | $[67, 67, -2w^{3} + w^{2} + 6w - 2]$ | $-\frac{3}{2}e^{13} + \frac{25}{2}e^{12} - \frac{43}{2}e^{11} - 80e^{10} + \frac{569}{2}e^{9} - \frac{1}{2}e^{8} - 892e^{7} + 704e^{6} + \frac{1789}{2}e^{5} - \frac{2429}{2}e^{4} - \frac{93}{2}e^{3} + \frac{1031}{2}e^{2} - \frac{301}{2}e + 2$ |
| 71 | $[71, 71, -2w^{3} + w^{2} + 7w - 3]$ | $\phantom{-}e^{13} - 12e^{12} + 39e^{11} + 38e^{10} - 399e^{9} + 371e^{8} + 1090e^{7} - 1827e^{6} - 778e^{5} + 2527e^{4} - 442e^{3} - 967e^{2} + 393e - 26$ |
| 71 | $[71, 71, 2w^{4} - 4w^{3} - 7w^{2} + 13w - 1]$ | $\phantom{-}\frac{1}{2}e^{13} - \frac{3}{2}e^{12} - \frac{23}{2}e^{11} + 43e^{10} + \frac{109}{2}e^{9} - \frac{635}{2}e^{8} + 11e^{7} + 897e^{6} - \frac{885}{2}e^{5} - \frac{2019}{2}e^{4} + \frac{1423}{2}e^{3} + \frac{661}{2}e^{2} - \frac{573}{2}e + 35$ |
| 73 | $[73, 73, -w^{4} + 2w^{3} + 3w^{2} - 7w]$ | $-\frac{1}{2}e^{13} + \frac{9}{2}e^{12} - \frac{17}{2}e^{11} - 31e^{10} + \frac{231}{2}e^{9} + \frac{35}{2}e^{8} - 414e^{7} + 217e^{6} + \frac{1179}{2}e^{5} - \frac{877}{2}e^{4} - \frac{645}{2}e^{3} + \frac{479}{2}e^{2} + \frac{91}{2}e - 22$ |
| 73 | $[73, 73, w^{4} + w^{3} - 3w^{2} - 4w - 2]$ | $-\frac{7}{2}e^{13} + \frac{53}{2}e^{12} - \frac{67}{2}e^{11} - 194e^{10} + \frac{1049}{2}e^{9} + \frac{465}{2}e^{8} - 1771e^{7} + 756e^{6} + \frac{4099}{2}e^{5} - \frac{3317}{2}e^{4} - \frac{1003}{2}e^{3} + \frac{1453}{2}e^{2} - \frac{351}{2}e + 6$ |
| 79 | $[79, 79, w^{4} - w^{3} - 5w^{2} + 4w + 6]$ | $-\frac{3}{4}e^{13} + \frac{17}{4}e^{12} + \frac{9}{4}e^{11} - 47e^{10} + \frac{127}{4}e^{9} + \frac{771}{4}e^{8} - 187e^{7} - \frac{773}{2}e^{6} + \frac{1483}{4}e^{5} + \frac{1605}{4}e^{4} - \frac{1191}{4}e^{3} - \frac{723}{4}e^{2} + \frac{305}{4}e + \frac{11}{2}$ |
| 83 | $[83, 83, -2w^{4} + w^{3} + 9w^{2} - 3w - 6]$ | $-3e^{13} + 24e^{12} - 40e^{11} - 147e^{10} + 529e^{9} - 59e^{8} - 1593e^{7} + 1498e^{6} + 1388e^{5} - 2407e^{4} + 297e^{3} + 905e^{2} - 456e + 48$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $43$ | $[43, 43, -w^{3} + 4w - 2]$ | $-1$ |