Base field 4.4.9301.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 4x^{7} - 10x^{6} + 53x^{5} - 4x^{4} - 146x^{3} + 72x^{2} + 70x - 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}\frac{14}{25}e^{7} - \frac{27}{25}e^{6} - \frac{187}{25}e^{5} + \frac{67}{5}e^{4} + \frac{529}{25}e^{3} - 29e^{2} - \frac{267}{25}e + \frac{93}{25}$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{26}{25}e^{7} - \frac{43}{25}e^{6} - \frac{358}{25}e^{5} + \frac{108}{5}e^{4} + \frac{1111}{25}e^{3} - 48e^{2} - \frac{703}{25}e + \frac{137}{25}$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}\frac{26}{25}e^{7} - \frac{43}{25}e^{6} - \frac{358}{25}e^{5} + \frac{108}{5}e^{4} + \frac{1111}{25}e^{3} - 48e^{2} - \frac{703}{25}e + \frac{137}{25}$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{21}{25}e^{7} + \frac{28}{25}e^{6} + \frac{293}{25}e^{5} - \frac{68}{5}e^{4} - \frac{931}{25}e^{3} + 26e^{2} + \frac{538}{25}e + \frac{48}{25}$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{2}{5}e^{7} - \frac{1}{5}e^{6} - \frac{31}{5}e^{5} + 2e^{4} + \frac{127}{5}e^{3} - \frac{136}{5}e - \frac{16}{5}$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 5w - 1]$ | $-\frac{14}{5}e^{7} + \frac{22}{5}e^{6} + \frac{192}{5}e^{5} - 54e^{4} - \frac{584}{5}e^{3} + 110e^{2} + \frac{327}{5}e - \frac{18}{5}$ |
| 37 | $[37, 37, -w^{3} + 4w + 1]$ | $\phantom{-}2e^{7} - 3e^{6} - 28e^{5} + 37e^{4} + 91e^{3} - 77e^{2} - 66e + 6$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 2w + 1]$ | $\phantom{-}\frac{11}{25}e^{7} - \frac{23}{25}e^{6} - \frac{138}{25}e^{5} + \frac{58}{5}e^{4} + \frac{296}{25}e^{3} - 27e^{2} + \frac{167}{25}e + \frac{207}{25}$ |
| 49 | $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ | $\phantom{-}\frac{24}{25}e^{7} - \frac{32}{25}e^{6} - \frac{342}{25}e^{5} + \frac{77}{5}e^{4} + \frac{1164}{25}e^{3} - 28e^{2} - \frac{897}{25}e - \frac{87}{25}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ | $-\frac{13}{25}e^{7} + \frac{9}{25}e^{6} + \frac{204}{25}e^{5} - \frac{19}{5}e^{4} - \frac{868}{25}e^{3} + 2e^{2} + \frac{1014}{25}e + \frac{244}{25}$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ | $-\frac{7}{25}e^{7} + \frac{1}{25}e^{6} + \frac{106}{25}e^{5} - \frac{1}{5}e^{4} - \frac{427}{25}e^{3} - 3e^{2} + \frac{446}{25}e + \frac{291}{25}$ |
| 67 | $[67, 67, w^{2} - 3w - 2]$ | $-\frac{6}{25}e^{7} + \frac{8}{25}e^{6} + \frac{73}{25}e^{5} - \frac{18}{5}e^{4} - \frac{141}{25}e^{3} + 6e^{2} - \frac{32}{25}e - \frac{147}{25}$ |
| 71 | $[71, 71, -w^{2} + 5]$ | $\phantom{-}\frac{19}{25}e^{7} - \frac{17}{25}e^{6} - \frac{277}{25}e^{5} + \frac{37}{5}e^{4} + \frac{1009}{25}e^{3} - 7e^{2} - \frac{957}{25}e - \frac{222}{25}$ |
| 71 | $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ | $-\frac{6}{25}e^{7} + \frac{33}{25}e^{6} + \frac{48}{25}e^{5} - \frac{88}{5}e^{4} + \frac{159}{25}e^{3} + 48e^{2} - \frac{657}{25}e - \frac{347}{25}$ |
| 71 | $[71, 71, w^{2} - 2w - 5]$ | $-\frac{56}{25}e^{7} + \frac{83}{25}e^{6} + \frac{798}{25}e^{5} - \frac{203}{5}e^{4} - \frac{2741}{25}e^{3} + 81e^{2} + \frac{2368}{25}e + \frac{128}{25}$ |
| 79 | $[79, 79, w^{2} - 3w - 1]$ | $-\frac{21}{25}e^{7} + \frac{28}{25}e^{6} + \frac{293}{25}e^{5} - \frac{68}{5}e^{4} - \frac{956}{25}e^{3} + 26e^{2} + \frac{713}{25}e - \frac{52}{25}$ |
| 79 | $[79, 79, w^{3} - 6w - 1]$ | $-\frac{37}{25}e^{7} + \frac{66}{25}e^{6} + \frac{496}{25}e^{5} - \frac{161}{5}e^{4} - \frac{1407}{25}e^{3} + 64e^{2} + \frac{611}{25}e + \frac{81}{25}$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ | $\phantom{-}\frac{33}{25}e^{7} - \frac{44}{25}e^{6} - \frac{464}{25}e^{5} + \frac{104}{5}e^{4} + \frac{1538}{25}e^{3} - 35e^{2} - \frac{1224}{25}e - \frac{229}{25}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |