Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, -w^{2} + 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 4x^{6} - 12x^{5} + 60x^{4} + 4x^{3} - 207x^{2} + 195x - 50\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{7}{25}e^{6} - \frac{18}{25}e^{5} - \frac{99}{25}e^{4} + 11e^{3} + \frac{253}{25}e^{2} - \frac{1009}{25}e + \frac{99}{5}$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $-\frac{11}{25}e^{6} + \frac{39}{25}e^{5} + \frac{152}{25}e^{4} - 23e^{3} - \frac{369}{25}e^{2} + \frac{2007}{25}e - \frac{182}{5}$ |
| 11 | $[11, 11, -w + 2]$ | $-\frac{4}{25}e^{6} + \frac{21}{25}e^{5} + \frac{53}{25}e^{4} - 13e^{3} - \frac{91}{25}e^{2} + \frac{1173}{25}e - \frac{98}{5}$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{22}{25}e^{6} + \frac{78}{25}e^{5} + \frac{304}{25}e^{4} - 47e^{3} - \frac{713}{25}e^{2} + \frac{4189}{25}e - \frac{394}{5}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-e^{2} + 6$ |
| 17 | $[17, 17, -w^{2} + w + 8]$ | $-\frac{11}{25}e^{6} + \frac{39}{25}e^{5} + \frac{152}{25}e^{4} - 24e^{3} - \frac{369}{25}e^{2} + \frac{2207}{25}e - \frac{192}{5}$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}\frac{28}{25}e^{6} - \frac{97}{25}e^{5} - \frac{396}{25}e^{4} + 59e^{3} + \frac{987}{25}e^{2} - \frac{5311}{25}e + \frac{496}{5}$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $\phantom{-}\frac{22}{25}e^{6} - \frac{78}{25}e^{5} - \frac{304}{25}e^{4} + 48e^{3} + \frac{713}{25}e^{2} - \frac{4414}{25}e + \frac{404}{5}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}1$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{3}{5}e^{6} - \frac{12}{5}e^{5} - \frac{41}{5}e^{4} + 37e^{3} + \frac{87}{5}e^{2} - \frac{681}{5}e + 68$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{3}{5}e^{6} - \frac{12}{5}e^{5} - \frac{41}{5}e^{4} + 36e^{3} + \frac{92}{5}e^{2} - \frac{631}{5}e + 58$ |
| 31 | $[31, 31, w^{2} - 2w - 8]$ | $\phantom{-}\frac{63}{25}e^{6} - \frac{212}{25}e^{5} - \frac{891}{25}e^{4} + 129e^{3} + \frac{2227}{25}e^{2} - \frac{11681}{25}e + \frac{1086}{5}$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $\phantom{-}e^{6} - 3e^{5} - 14e^{4} + 45e^{3} + 36e^{2} - 161e + 72$ |
| 41 | $[41, 41, -w - 4]$ | $\phantom{-}\frac{14}{25}e^{6} - \frac{61}{25}e^{5} - \frac{198}{25}e^{4} + 38e^{3} + \frac{456}{25}e^{2} - \frac{3518}{25}e + \frac{318}{5}$ |
| 41 | $[41, 41, w^{2} - 2w - 7]$ | $-\frac{71}{25}e^{6} + \frac{229}{25}e^{5} + \frac{997}{25}e^{4} - 138e^{3} - \frac{2509}{25}e^{2} + \frac{12377}{25}e - \frac{1132}{5}$ |
| 47 | $[47, 47, 2w^{2} - 3w - 7]$ | $\phantom{-}\frac{9}{25}e^{6} - \frac{41}{25}e^{5} - \frac{113}{25}e^{4} + 25e^{3} + \frac{161}{25}e^{2} - \frac{2258}{25}e + \frac{248}{5}$ |
| 53 | $[53, 53, -w^{2} + w + 9]$ | $-\frac{12}{25}e^{6} + \frac{38}{25}e^{5} + \frac{159}{25}e^{4} - 24e^{3} - \frac{273}{25}e^{2} + \frac{2319}{25}e - \frac{284}{5}$ |
| 61 | $[61, 61, 3w^{2} - 2w - 17]$ | $-\frac{28}{25}e^{6} + \frac{122}{25}e^{5} + \frac{371}{25}e^{4} - 75e^{3} - \frac{662}{25}e^{2} + \frac{6836}{25}e - \frac{686}{5}$ |
| 67 | $[67, 67, 2w - 1]$ | $\phantom{-}\frac{7}{25}e^{6} - \frac{18}{25}e^{5} - \frac{99}{25}e^{4} + 11e^{3} + \frac{228}{25}e^{2} - \frac{1009}{25}e + \frac{134}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{2} + 3]$ | $-1$ |