Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, w^{2} - 2w - 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 5x^{7} - 13x^{6} + 79x^{5} + 25x^{4} - 312x^{3} + 320x + 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 2]$ | $-1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 2]$ | $-\frac{13}{344}e^{7} + \frac{123}{344}e^{6} - \frac{49}{344}e^{5} - \frac{1933}{344}e^{4} + \frac{2729}{344}e^{3} + \frac{3753}{172}e^{2} - \frac{1095}{43}e - \frac{960}{43}$ |
| 7 | $[7, 7, -w + 1]$ | $-\frac{25}{172}e^{7} + \frac{225}{344}e^{6} + \frac{655}{344}e^{5} - \frac{3257}{344}e^{4} - \frac{1137}{344}e^{3} + \frac{10151}{344}e^{2} - \frac{239}{43}e - \frac{550}{43}$ |
| 8 | $[8, 2, 2]$ | $-\frac{57}{344}e^{7} + \frac{139}{172}e^{6} + \frac{177}{86}e^{5} - \frac{524}{43}e^{4} - \frac{363}{172}e^{3} + \frac{14325}{344}e^{2} - \frac{999}{86}e - \frac{1057}{43}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{29}{43}e^{7} + \frac{1259}{344}e^{6} + \frac{2377}{344}e^{5} - \frac{18967}{344}e^{4} + \frac{4045}{344}e^{3} + \frac{65355}{344}e^{2} - \frac{4518}{43}e - \frac{5476}{43}$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-\frac{407}{688}e^{7} + \frac{2369}{688}e^{6} + \frac{3573}{688}e^{5} - \frac{35935}{688}e^{4} + \frac{15395}{688}e^{3} + \frac{63331}{344}e^{2} - \frac{5354}{43}e - \frac{5872}{43}$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}\frac{123}{172}e^{7} - \frac{176}{43}e^{6} - \frac{567}{86}e^{5} + \frac{5349}{86}e^{4} - \frac{990}{43}e^{3} - \frac{37561}{172}e^{2} + \frac{6071}{43}e + \frac{6662}{43}$ |
| 27 | $[27, 3, 3]$ | $-\frac{237}{344}e^{7} + \frac{1389}{344}e^{6} + \frac{2077}{344}e^{5} - \frac{21103}{344}e^{4} + \frac{9087}{344}e^{3} + \frac{18477}{86}e^{2} - \frac{6335}{43}e - \frac{6606}{43}$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-\frac{141}{172}e^{7} + \frac{371}{86}e^{6} + \frac{379}{43}e^{5} - \frac{2778}{43}e^{4} + \frac{727}{86}e^{3} + \frac{37581}{172}e^{2} - \frac{4714}{43}e - \frac{5854}{43}$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{463}{688}e^{7} - \frac{2449}{688}e^{6} - \frac{5029}{688}e^{5} + \frac{36879}{688}e^{4} - \frac{3891}{688}e^{3} - \frac{62999}{344}e^{2} + \frac{3730}{43}e + \frac{4976}{43}$ |
| 37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{31}{172}e^{7} - \frac{161}{172}e^{6} - \frac{333}{172}e^{5} + \frac{2347}{172}e^{4} - \frac{223}{172}e^{3} - \frac{3677}{86}e^{2} + \frac{790}{43}e + \frac{940}{43}$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-\frac{47}{172}e^{7} + \frac{509}{344}e^{6} + \frac{939}{344}e^{5} - \frac{7709}{344}e^{4} + \frac{2331}{344}e^{3} + \frac{26903}{344}e^{2} - \frac{2245}{43}e - \frac{2238}{43}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{31}{172}e^{7} + \frac{161}{172}e^{6} + \frac{333}{172}e^{5} - \frac{2347}{172}e^{4} + \frac{223}{172}e^{3} + \frac{3677}{86}e^{2} - \frac{833}{43}e - \frac{854}{43}$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $\phantom{-}\frac{219}{344}e^{7} - \frac{1179}{344}e^{6} - \frac{2211}{344}e^{5} + \frac{17593}{344}e^{4} - \frac{4369}{344}e^{3} - \frac{14903}{86}e^{2} + \frac{4498}{43}e + \frac{5032}{43}$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}\frac{249}{172}e^{7} - \frac{350}{43}e^{6} - \frac{1173}{86}e^{5} + \frac{10539}{86}e^{4} - \frac{1786}{43}e^{3} - \frac{72875}{172}e^{2} + \frac{11493}{43}e + \frac{13046}{43}$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $\phantom{-}\frac{77}{86}e^{7} - \frac{865}{172}e^{6} - \frac{1467}{172}e^{5} + \frac{13045}{172}e^{4} - \frac{4183}{172}e^{3} - \frac{45087}{172}e^{2} + \frac{6861}{43}e + \frac{7946}{43}$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $-\frac{74}{43}e^{7} + \frac{1633}{172}e^{6} + \frac{2923}{172}e^{5} - \frac{24653}{172}e^{4} + \frac{6783}{172}e^{3} + \frac{85617}{172}e^{2} - \frac{12792}{43}e - \frac{14768}{43}$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{31}{344}e^{7} - \frac{161}{344}e^{6} - \frac{333}{344}e^{5} + \frac{2519}{344}e^{4} - \frac{739}{344}e^{3} - \frac{4795}{172}e^{2} + \frac{954}{43}e + \frac{986}{43}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w - 1]$ | $-1$ |
| $5$ | $[5, 5, w + 2]$ | $1$ |