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: | $[9,9,w + 7]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $80$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 22x^{14} + 191x^{12} + 835x^{10} + 1951x^{8} + 2395x^{6} + 1435x^{4} + 355x^{2} + 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{11}{87}e^{15} - \frac{230}{87}e^{13} - \frac{1858}{87}e^{11} - \frac{7253}{87}e^{9} - \frac{13865}{87}e^{7} - \frac{11180}{87}e^{5} - \frac{1730}{87}e^{3} + \frac{790}{87}e$ |
| 7 | $[7, 7, -2w + 15]$ | $\phantom{-}\frac{1}{29}e^{14} + \frac{13}{29}e^{12} + \frac{45}{29}e^{10} - \frac{34}{29}e^{8} - \frac{382}{29}e^{6} - \frac{373}{29}e^{4} + \frac{181}{29}e^{2} + \frac{118}{29}$ |
| 7 | $[7, 7, -2w - 15]$ | $\phantom{-}\frac{3}{29}e^{14} + \frac{68}{29}e^{12} + \frac{599}{29}e^{10} + \frac{2595}{29}e^{8} + \frac{5756}{29}e^{6} + \frac{6073}{29}e^{4} + \frac{2312}{29}e^{2} + \frac{64}{29}$ |
| 11 | $[11, 11, w + 5]$ | $-\frac{31}{87}e^{15} - \frac{664}{87}e^{13} - \frac{5513}{87}e^{11} - \frac{22291}{87}e^{9} - \frac{44998}{87}e^{7} - \frac{40666}{87}e^{5} - \frac{11005}{87}e^{3} + \frac{692}{87}e$ |
| 11 | $[11, 11, w + 6]$ | $-\frac{11}{87}e^{15} - \frac{230}{87}e^{13} - \frac{1858}{87}e^{11} - \frac{7253}{87}e^{9} - \frac{13865}{87}e^{7} - \frac{11180}{87}e^{5} - \frac{1643}{87}e^{3} + \frac{1138}{87}e$ |
| 19 | $[19, 19, w + 1]$ | $-\frac{7}{29}e^{15} - \frac{149}{29}e^{13} - \frac{1243}{29}e^{11} - \frac{5156}{29}e^{9} - \frac{11159}{29}e^{7} - \frac{12092}{29}e^{5} - \frac{5733}{29}e^{3} - \frac{710}{29}e$ |
| 19 | $[19, 19, w + 18]$ | $-\frac{34}{29}e^{15} - \frac{732}{29}e^{13} - \frac{6141}{29}e^{11} - \frac{25350}{29}e^{9} - \frac{53451}{29}e^{7} - \frac{53670}{29}e^{5} - \frac{20741}{29}e^{3} - \frac{1692}{29}e$ |
| 23 | $[23, 23, w + 9]$ | $-\frac{10}{29}e^{14} - \frac{217}{29}e^{12} - \frac{1813}{29}e^{10} - \frac{7345}{29}e^{8} - \frac{14943}{29}e^{6} - \frac{14192}{29}e^{4} - \frac{5116}{29}e^{2} - \frac{368}{29}$ |
| 23 | $[23, 23, -w + 9]$ | $-\frac{21}{29}e^{14} - \frac{447}{29}e^{12} - \frac{3700}{29}e^{10} - \frac{15033}{29}e^{8} - \frac{31099}{29}e^{6} - \frac{30389}{29}e^{4} - \frac{10935}{29}e^{2} - \frac{506}{29}$ |
| 25 | $[25, 5, 5]$ | $-\frac{4}{29}e^{14} - \frac{81}{29}e^{12} - \frac{644}{29}e^{10} - \frac{2532}{29}e^{8} - \frac{5055}{29}e^{6} - \frac{4714}{29}e^{4} - \frac{1739}{29}e^{2} - \frac{182}{29}$ |
| 29 | $[29, 29, w]$ | $-\frac{4}{29}e^{15} - \frac{81}{29}e^{13} - \frac{615}{29}e^{11} - \frac{2126}{29}e^{9} - \frac{3054}{29}e^{7} - \frac{393}{29}e^{5} + \frac{2321}{29}e^{3} + \frac{1065}{29}e$ |
| 37 | $[37, 37, w + 13]$ | $\phantom{-}\frac{95}{87}e^{15} + \frac{2018}{87}e^{13} + \frac{16687}{87}e^{11} + \frac{67820}{87}e^{9} + \frac{140726}{87}e^{7} + \frac{139667}{87}e^{5} + \frac{55301}{87}e^{3} + \frac{5903}{87}e$ |
| 37 | $[37, 37, w + 24]$ | $\phantom{-}\frac{1}{87}e^{15} + \frac{13}{87}e^{13} + \frac{74}{87}e^{11} + \frac{343}{87}e^{9} + \frac{1300}{87}e^{7} + \frac{2962}{87}e^{5} + \frac{3574}{87}e^{3} + \frac{1771}{87}e$ |
| 43 | $[43, 43, w + 12]$ | $-\frac{83}{87}e^{15} - \frac{1775}{87}e^{13} - \frac{14755}{87}e^{11} - \frac{60224}{87}e^{9} - \frac{125561}{87}e^{7} - \frac{125525}{87}e^{5} - \frac{50084}{87}e^{3} - \frac{5444}{87}e$ |
| 43 | $[43, 43, w + 31]$ | $\phantom{-}\frac{17}{87}e^{15} + \frac{395}{87}e^{13} + \frac{3607}{87}e^{11} + \frac{16445}{87}e^{9} + \frac{39239}{87}e^{7} + \frac{46439}{87}e^{5} + \frac{22478}{87}e^{3} + \frac{2354}{87}e$ |
| 61 | $[61, 61, w + 27]$ | $\phantom{-}\frac{32}{87}e^{15} + \frac{677}{87}e^{13} + \frac{5500}{87}e^{11} + \frac{21503}{87}e^{9} + \frac{41426}{87}e^{7} + \frac{35537}{87}e^{5} + \frac{10403}{87}e^{3} + \frac{1253}{87}e$ |
| 61 | $[61, 61, w + 34]$ | $\phantom{-}\frac{67}{87}e^{15} + \frac{1393}{87}e^{13} + \frac{11222}{87}e^{11} + \frac{44035}{87}e^{9} + \frac{86491}{87}e^{7} + \frac{77089}{87}e^{5} + \frac{22393}{87}e^{3} - \frac{533}{87}e$ |
| 71 | $[71, 71, 12w - 91]$ | $\phantom{-}\frac{5}{29}e^{14} + \frac{94}{29}e^{12} + \frac{689}{29}e^{10} + \frac{2527}{29}e^{8} + \frac{4963}{29}e^{6} + \frac{5095}{29}e^{4} + \frac{2268}{29}e^{2} + \frac{184}{29}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 2]$ | $-1$ |