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: | $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 6x^{9} - 2x^{8} + 70x^{7} - 78x^{6} - 244x^{5} + 424x^{4} + 238x^{3} - 655x^{2} + 70x + 190\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w + 1]$ | $-\frac{1}{4}e^{9} + \frac{5}{4}e^{8} + \frac{7}{4}e^{7} - \frac{61}{4}e^{6} + \frac{11}{4}e^{5} + \frac{239}{4}e^{4} - \frac{129}{4}e^{3} - \frac{349}{4}e^{2} + 44e + \frac{69}{2}$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-\frac{1}{4}e^{9} + \frac{3}{4}e^{8} + \frac{11}{4}e^{7} - \frac{35}{4}e^{6} - \frac{33}{4}e^{5} + \frac{125}{4}e^{4} + \frac{15}{4}e^{3} - \frac{151}{4}e^{2} + 8e + \frac{19}{2}$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $-\frac{1}{2}e^{9} + \frac{9}{4}e^{8} + \frac{9}{2}e^{7} - \frac{115}{4}e^{6} - \frac{9}{2}e^{5} + \frac{477}{4}e^{4} - 38e^{3} - \frac{721}{4}e^{2} + \frac{143}{2}e + \frac{131}{2}$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{4}e^{9} + \frac{3}{4}e^{8} + \frac{11}{4}e^{7} - \frac{33}{4}e^{6} - \frac{37}{4}e^{5} + \frac{105}{4}e^{4} + \frac{47}{4}e^{3} - \frac{97}{4}e^{2} - 4e - \frac{1}{2}$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{1}{4}e^{9} + \frac{3}{4}e^{8} + \frac{13}{4}e^{7} - \frac{37}{4}e^{6} - \frac{57}{4}e^{5} + \frac{141}{4}e^{4} + \frac{97}{4}e^{3} - \frac{173}{4}e^{2} - 10e + \frac{13}{2}$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ | $-1$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 5w - 1]$ | $-\frac{1}{4}e^{9} + e^{8} + \frac{11}{4}e^{7} - \frac{27}{2}e^{6} - \frac{29}{4}e^{5} + \frac{119}{2}e^{4} - \frac{27}{4}e^{3} - 93e^{2} + \frac{65}{2}e + 33$ |
| 37 | $[37, 37, -w^{3} + 4w + 1]$ | $-\frac{3}{2}e^{9} + 6e^{8} + 15e^{7} - 76e^{6} - \frac{63}{2}e^{5} + 311e^{4} - 48e^{3} - 462e^{2} + 144e + 160$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 2w + 1]$ | $-e^{9} + 4e^{8} + \frac{19}{2}e^{7} - 50e^{6} - 15e^{5} + 201e^{4} - \frac{105}{2}e^{3} - 293e^{2} + 113e + 104$ |
| 49 | $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ | $-\frac{1}{2}e^{9} + \frac{11}{4}e^{8} + 3e^{7} - \frac{137}{4}e^{6} + \frac{23}{2}e^{5} + \frac{551}{4}e^{4} - \frac{171}{2}e^{3} - \frac{823}{4}e^{2} + \frac{221}{2}e + \frac{169}{2}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ | $-e^{9} + 4e^{8} + 10e^{7} - 51e^{6} - 21e^{5} + 210e^{4} - 31e^{3} - 307e^{2} + 90e + 94$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ | $-\frac{1}{4}e^{9} + e^{8} + \frac{9}{4}e^{7} - 12e^{6} - \frac{13}{4}e^{5} + \frac{91}{2}e^{4} - \frac{41}{4}e^{3} - \frac{125}{2}e^{2} + \frac{37}{2}e + 28$ |
| 67 | $[67, 67, w^{2} - 3w - 2]$ | $\phantom{-}e^{9} - \frac{17}{4}e^{8} - \frac{19}{2}e^{7} + \frac{215}{4}e^{6} + 16e^{5} - \frac{881}{4}e^{4} + 47e^{3} + \frac{1313}{4}e^{2} - \frac{223}{2}e - \frac{219}{2}$ |
| 71 | $[71, 71, -w^{2} + 5]$ | $-\frac{1}{4}e^{9} + \frac{1}{4}e^{8} + \frac{17}{4}e^{7} - \frac{17}{4}e^{6} - \frac{93}{4}e^{5} + \frac{91}{4}e^{4} + \frac{173}{4}e^{3} - \frac{157}{4}e^{2} - 13e + \frac{17}{2}$ |
| 71 | $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ | $-\frac{1}{2}e^{9} + \frac{3}{2}e^{8} + \frac{11}{2}e^{7} - \frac{33}{2}e^{6} - \frac{37}{2}e^{5} + \frac{105}{2}e^{4} + \frac{47}{2}e^{3} - \frac{101}{2}e^{2} - 10e + 11$ |
| 71 | $[71, 71, w^{2} - 2w - 5]$ | $\phantom{-}\frac{7}{4}e^{9} - 7e^{8} - \frac{69}{4}e^{7} + 89e^{6} + \frac{131}{4}e^{5} - \frac{733}{2}e^{4} + \frac{301}{4}e^{3} + \frac{1099}{2}e^{2} - \frac{389}{2}e - 200$ |
| 79 | $[79, 79, w^{2} - 3w - 1]$ | $\phantom{-}2e^{9} - \frac{31}{4}e^{8} - 20e^{7} + \frac{387}{4}e^{6} + 43e^{5} - \frac{1551}{4}e^{4} + \frac{107}{2}e^{3} + \frac{2249}{4}e^{2} - \frac{329}{2}e - \frac{391}{2}$ |
| 79 | $[79, 79, w^{3} - 6w - 1]$ | $-\frac{3}{4}e^{9} + \frac{13}{4}e^{8} + \frac{27}{4}e^{7} - \frac{167}{4}e^{6} - \frac{23}{4}e^{5} + \frac{699}{4}e^{4} - \frac{257}{4}e^{3} - \frac{1079}{4}e^{2} + 121e + \frac{211}{2}$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ | $-\frac{1}{2}e^{9} + 2e^{8} + \frac{9}{2}e^{7} - 25e^{6} - \frac{9}{2}e^{5} + 103e^{4} - \frac{77}{2}e^{3} - 164e^{2} + 73e + 74$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ | $1$ |