Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + x^{6} - 14x^{5} - 9x^{4} + 56x^{3} + 20x^{2} - 64x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}\frac{3}{4}e^{6} + \frac{9}{4}e^{5} - 7e^{4} - \frac{87}{4}e^{3} + \frac{19}{2}e^{2} + 41e + 10$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-\frac{3}{2}e^{6} - 4e^{5} + \frac{29}{2}e^{4} + \frac{75}{2}e^{3} - \frac{45}{2}e^{2} - 68e - 19$ |
| 13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $-\frac{3}{4}e^{6} - \frac{9}{4}e^{5} + 7e^{4} + \frac{87}{4}e^{3} - \frac{19}{2}e^{2} - 41e - 10$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}2e^{6} + 5e^{5} - 20e^{4} - 47e^{3} + 35e^{2} + 85e + 17$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{11}{4}e^{6} - \frac{29}{4}e^{5} + 27e^{4} + \frac{275}{4}e^{3} - \frac{91}{2}e^{2} - 127e - 24$ |
| 19 | $[19, 19, w^{3} - 5w]$ | $\phantom{-}\frac{7}{4}e^{6} + \frac{9}{2}e^{5} - \frac{69}{4}e^{4} - \frac{171}{4}e^{3} + \frac{117}{4}e^{2} + \frac{161}{2}e + 14$ |
| 19 | $[19, 19, -w + 3]$ | $-\frac{1}{2}e^{6} - \frac{3}{2}e^{5} + 5e^{4} + \frac{29}{2}e^{3} - 10e^{2} - 27e - 3$ |
| 23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}\frac{3}{4}e^{6} + \frac{9}{4}e^{5} - 7e^{4} - \frac{87}{4}e^{3} + \frac{17}{2}e^{2} + 39e + 16$ |
| 25 | $[25, 5, w^{2} - 3]$ | $-\frac{3}{4}e^{6} - \frac{5}{2}e^{5} + \frac{25}{4}e^{4} + \frac{99}{4}e^{3} - \frac{9}{4}e^{2} - \frac{99}{2}e - 20$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $\phantom{-}2e^{6} + \frac{19}{4}e^{5} - \frac{79}{4}e^{4} - 44e^{3} + \frac{129}{4}e^{2} + \frac{157}{2}e + 18$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $-\frac{1}{2}e^{6} - \frac{1}{2}e^{5} + 6e^{4} + \frac{9}{2}e^{3} - 16e^{2} - 10e + 2$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}e^{3} + 2e^{2} - 7e - 4$ |
| 47 | $[47, 47, w^{3} - 6w + 1]$ | $\phantom{-}\frac{3}{4}e^{6} + \frac{7}{4}e^{5} - \frac{15}{2}e^{4} - \frac{63}{4}e^{3} + 14e^{2} + 27e - 1$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{7}{2}e^{6} - \frac{17}{2}e^{5} + 35e^{4} + \frac{159}{2}e^{3} - 62e^{2} - 144e - 27$ |
| 67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $-\frac{11}{4}e^{6} - \frac{27}{4}e^{5} + \frac{55}{2}e^{4} + \frac{255}{4}e^{3} - 48e^{2} - 116e - 26$ |
| 67 | $[67, 67, w^{3} - 7w + 3]$ | $\phantom{-}\frac{5}{2}e^{6} + 7e^{5} - \frac{47}{2}e^{4} - \frac{133}{2}e^{3} + \frac{67}{2}e^{2} + 125e + 30$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $\phantom{-}\frac{5}{4}e^{6} + \frac{13}{4}e^{5} - \frac{23}{2}e^{4} - \frac{121}{4}e^{3} + 14e^{2} + 58e + 18$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{11}{4}e^{6} + \frac{31}{4}e^{5} - \frac{55}{2}e^{4} - \frac{299}{4}e^{3} + 51e^{2} + 140e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $-1$ |