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: | $[23, 23, -w^{3} + w^{2} + 3w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 2x^{6} - 26x^{5} + 32x^{4} + 160x^{3} - 72x^{2} - 112x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 6w^{2} - 2w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - w - 4]$ | $-\frac{31}{392}e^{6} + \frac{29}{196}e^{5} + \frac{201}{98}e^{4} - \frac{211}{98}e^{3} - \frac{86}{7}e^{2} + \frac{97}{49}e + \frac{260}{49}$ |
| 11 | $[11, 11, -2w^{4} + w^{3} + 10w^{2} + w - 3]$ | $-\frac{17}{392}e^{6} + \frac{2}{49}e^{5} + \frac{241}{196}e^{4} - \frac{43}{98}e^{3} - \frac{58}{7}e^{2} - \frac{29}{49}e + \frac{288}{49}$ |
| 11 | $[11, 11, w^{4} - 6w^{2} - 3w + 3]$ | $-\frac{1}{392}e^{6} + \frac{3}{49}e^{5} - \frac{3}{98}e^{4} - \frac{69}{49}e^{3} + \frac{15}{14}e^{2} + \frac{324}{49}e - \frac{58}{49}$ |
| 17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}\frac{1}{392}e^{6} - \frac{3}{49}e^{5} + \frac{3}{98}e^{4} + \frac{69}{49}e^{3} - \frac{4}{7}e^{2} - \frac{324}{49}e - \frac{40}{49}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w]$ | $\phantom{-}1$ |
| 27 | $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ | $-\frac{1}{14}e^{6} + \frac{3}{14}e^{5} + \frac{23}{14}e^{4} - \frac{55}{14}e^{3} - 8e^{2} + \frac{92}{7}e + \frac{20}{7}$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ | $-\frac{1}{28}e^{6} + \frac{3}{28}e^{5} + \frac{23}{28}e^{4} - \frac{31}{14}e^{3} - 4e^{2} + \frac{74}{7}e + \frac{24}{7}$ |
| 32 | $[32, 2, -2]$ | $\phantom{-}\frac{13}{392}e^{6} - \frac{9}{196}e^{5} - \frac{167}{196}e^{4} + \frac{15}{49}e^{3} + \frac{39}{7}e^{2} + \frac{149}{49}e - \frac{275}{49}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{9}{98}e^{6} - \frac{10}{49}e^{5} - \frac{235}{98}e^{4} + \frac{181}{49}e^{3} + \frac{101}{7}e^{2} - \frac{688}{49}e - \frac{362}{49}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $\phantom{-}\frac{1}{392}e^{6} - \frac{3}{49}e^{5} + \frac{3}{98}e^{4} + \frac{69}{49}e^{3} - \frac{1}{14}e^{2} - \frac{324}{49}e - \frac{138}{49}$ |
| 53 | $[53, 53, -w^{4} + 7w^{2} - 3]$ | $\phantom{-}\frac{53}{392}e^{6} - \frac{12}{49}e^{5} - \frac{331}{98}e^{4} + \frac{178}{49}e^{3} + \frac{131}{7}e^{2} - \frac{365}{49}e - \frac{258}{49}$ |
| 53 | $[53, 53, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 2]$ | $\phantom{-}\frac{5}{392}e^{6} - \frac{11}{196}e^{5} - \frac{17}{49}e^{4} + \frac{51}{49}e^{3} + \frac{22}{7}e^{2} - \frac{101}{49}e - \frac{200}{49}$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 16w^{2} + 8]$ | $\phantom{-}\frac{31}{196}e^{6} - \frac{29}{98}e^{5} - \frac{201}{49}e^{4} + \frac{211}{49}e^{3} + \frac{337}{14}e^{2} - \frac{243}{49}e - \frac{324}{49}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 4w - 3]$ | $\phantom{-}\frac{25}{196}e^{6} - \frac{61}{196}e^{5} - \frac{291}{98}e^{4} + \frac{481}{98}e^{3} + \frac{101}{7}e^{2} - \frac{520}{49}e + \frac{58}{49}$ |
| 73 | $[73, 73, 2w^{4} - 12w^{2} - 4w + 5]$ | $-\frac{29}{196}e^{6} + \frac{59}{196}e^{5} + \frac{365}{98}e^{4} - \frac{229}{49}e^{3} - \frac{285}{14}e^{2} + \frac{368}{49}e + \frac{66}{49}$ |
| 83 | $[83, 83, w^{4} - 5w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{392}e^{6} - \frac{3}{49}e^{5} + \frac{3}{98}e^{4} + \frac{69}{49}e^{3} - \frac{15}{14}e^{2} - \frac{422}{49}e + \frac{156}{49}$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-\frac{1}{98}e^{6} - \frac{1}{196}e^{5} + \frac{37}{98}e^{4} + \frac{18}{49}e^{3} - \frac{26}{7}e^{2} - \frac{125}{49}e + \frac{552}{49}$ |
| 103 | $[103, 103, 2w^{3} - 3w^{2} - 7w + 3]$ | $-\frac{11}{196}e^{6} + \frac{19}{196}e^{5} + \frac{65}{49}e^{4} - \frac{48}{49}e^{3} - \frac{45}{7}e^{2} - \frac{271}{49}e - \frac{2}{49}$ |
| 109 | $[109, 109, -3w^{4} + 2w^{3} + 14w^{2} + w - 6]$ | $-\frac{3}{28}e^{6} + \frac{9}{28}e^{5} + \frac{19}{7}e^{4} - \frac{43}{7}e^{3} - \frac{33}{2}e^{2} + \frac{138}{7}e + \frac{100}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{3} + w^{2} + 3w]$ | $-1$ |