Base field \(\Q(\sqrt{58}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w + 1]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} + 26x^{12} + 275x^{10} + 1529x^{8} + 4813x^{6} + 8565x^{4} + 7991x^{2} + 3025\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{3}{1265}e^{13} + \frac{188}{1265}e^{11} + \frac{56}{23}e^{9} + \frac{1982}{115}e^{7} + \frac{74664}{1265}e^{5} + \frac{23905}{253}e^{3} + \frac{70558}{1265}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{452}{1265}e^{13} - \frac{11037}{1265}e^{11} - \frac{1936}{23}e^{9} - \frac{46848}{115}e^{7} - \frac{1305211}{1265}e^{5} - \frac{323903}{253}e^{3} - \frac{765847}{1265}e$ |
| 7 | $[7, 7, -2w + 15]$ | $\phantom{-}\frac{11}{23}e^{12} + \frac{260}{23}e^{10} + \frac{2423}{23}e^{8} + \frac{11347}{23}e^{6} + \frac{28036}{23}e^{4} + \frac{34478}{23}e^{2} + \frac{16469}{23}$ |
| 7 | $[7, 7, -2w - 15]$ | $-\frac{18}{23}e^{12} - \frac{438}{23}e^{10} - \frac{4220}{23}e^{8} - \frac{20481}{23}e^{6} - \frac{52384}{23}e^{4} - \frac{66319}{23}e^{2} - \frac{32371}{23}$ |
| 11 | $[11, 11, w + 5]$ | $-\frac{186}{1265}e^{13} - \frac{4066}{1265}e^{11} - \frac{620}{23}e^{9} - \frac{12599}{115}e^{7} - \frac{283893}{1265}e^{5} - \frac{54684}{253}e^{3} - \frac{92571}{1265}e$ |
| 11 | $[11, 11, w + 6]$ | $\phantom{-}\frac{1396}{1265}e^{13} + \frac{33931}{1265}e^{11} + \frac{5926}{23}e^{9} + \frac{142974}{115}e^{7} + \frac{3985173}{1265}e^{5} + \frac{995866}{253}e^{3} + \frac{2392451}{1265}e$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{187}{115}e^{13} + \frac{4512}{115}e^{11} + \frac{8597}{23}e^{9} + \frac{205618}{115}e^{7} + \frac{516701}{115}e^{5} + \frac{128256}{23}e^{3} + \frac{306837}{115}e$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}\frac{58}{115}e^{13} + \frac{1373}{115}e^{11} + \frac{2556}{23}e^{9} + \frac{59447}{115}e^{7} + \frac{144464}{115}e^{5} + \frac{34417}{23}e^{3} + \frac{78038}{115}e$ |
| 23 | $[23, 23, w + 9]$ | $-\frac{49}{23}e^{12} - \frac{1177}{23}e^{10} - \frac{11153}{23}e^{8} - \frac{53013}{23}e^{6} - \frac{132210}{23}e^{4} - \frac{162466}{23}e^{2} - \frac{76630}{23}$ |
| 23 | $[23, 23, -w + 9]$ | $-e^{12} - 25e^{10} - 248e^{8} - 1240e^{6} - 3262e^{4} - 4230e^{2} - 2105$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{35}{23}e^{12} + \frac{844}{23}e^{10} + \frac{8042}{23}e^{8} + \frac{38517}{23}e^{6} + \frac{97038}{23}e^{4} + \frac{120841}{23}e^{2} + \frac{57936}{23}$ |
| 29 | $[29, 29, w]$ | $-\frac{9}{23}e^{13} - \frac{219}{23}e^{11} - \frac{2110}{23}e^{9} - \frac{10252}{23}e^{7} - \frac{26353}{23}e^{5} - \frac{33815}{23}e^{3} - \frac{16933}{23}e$ |
| 37 | $[37, 37, w + 13]$ | $-\frac{1778}{1265}e^{13} - \frac{42268}{1265}e^{11} - \frac{7207}{23}e^{9} - \frac{169757}{115}e^{7} - \frac{4633594}{1265}e^{5} - \frac{1141570}{253}e^{3} - \frac{2724658}{1265}e$ |
| 37 | $[37, 37, w + 24]$ | $-\frac{1467}{1265}e^{13} - \frac{35007}{1265}e^{11} - \frac{5994}{23}e^{9} - \frac{141773}{115}e^{7} - \frac{3882551}{1265}e^{5} - \frac{957791}{253}e^{3} - \frac{2280782}{1265}e$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}\frac{2617}{1265}e^{13} + \frac{63642}{1265}e^{11} + \frac{11123}{23}e^{9} + \frac{268618}{115}e^{7} + \frac{7495966}{1265}e^{5} + \frac{1875261}{253}e^{3} + \frac{4509137}{1265}e$ |
| 43 | $[43, 43, w + 31]$ | $\phantom{-}\frac{2223}{1265}e^{13} + \frac{53288}{1265}e^{11} + \frac{9158}{23}e^{9} + \frac{217002}{115}e^{7} + \frac{5932834}{1265}e^{5} + \frac{1453295}{253}e^{3} + \frac{3420323}{1265}e$ |
| 61 | $[61, 61, w + 27]$ | $\phantom{-}\frac{1159}{1265}e^{13} + \frac{27934}{1265}e^{11} + \frac{4837}{23}e^{9} + \frac{115886}{115}e^{7} + \frac{3222617}{1265}e^{5} + \frac{810567}{253}e^{3} + \frac{1982099}{1265}e$ |
| 61 | $[61, 61, w + 34]$ | $-\frac{1709}{1265}e^{13} - \frac{41739}{1265}e^{11} - \frac{7322}{23}e^{9} - \frac{177186}{115}e^{7} - \frac{4937792}{1265}e^{5} - \frac{1226532}{253}e^{3} - \frac{2908244}{1265}e$ |
| 71 | $[71, 71, 12w - 91]$ | $-\frac{30}{23}e^{12} - \frac{730}{23}e^{10} - \frac{7018}{23}e^{8} - \frac{33836}{23}e^{6} - \frac{85298}{23}e^{4} - \frac{105165}{23}e^{2} - \frac{49367}{23}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-\frac{3}{1265}e^{13} - \frac{188}{1265}e^{11} - \frac{56}{23}e^{9} - \frac{1982}{115}e^{7} - \frac{74664}{1265}e^{5} - \frac{23905}{253}e^{3} - \frac{70558}{1265}e$ |