Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $135$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} + x^{19} + 17x^{18} + 2x^{17} + 248x^{16} + 995x^{15} + 4989x^{14} + 13282x^{13} + 63507x^{12} + 127079x^{11} + 239988x^{10} + 385912x^{9} + 643652x^{8} + 204532x^{7} + 120869x^{6} + 48254x^{5} + 17662x^{4} - 3597x^{3} + 1062x^{2} - 135x + 81\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 7]$ | $...$ |
| 29 | $[29, 29, w + 6]$ | $...$ |
| 29 | $[29, 29, w + 22]$ | $...$ |
| 41 | $[41, 41, w + 13]$ | $...$ |
| 41 | $[41, 41, w + 27]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 47 | $[47, 47, w + 2]$ | $...$ |
| 47 | $[47, 47, w + 44]$ | $...$ |
| 73 | $[73, 73, w + 33]$ | $...$ |
| 73 | $[73, 73, w + 39]$ | $...$ |
| 83 | $[83, 83, -4w - 37]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{13550072768601956}{5134046535336719817}e^{19} + \frac{13540425610963436}{5134046535336719817}e^{18} + \frac{230187235386378412}{5134046535336719817}e^{17} + \frac{27080851221926872}{5134046535336719817}e^{16} + \frac{3358025551518932128}{5134046535336719817}e^{15} + \frac{13484627570112399373}{5134046535336719817}e^{14} + \frac{22517727791032194068}{1711348845112239939}e^{13} + \frac{179843932964816356952}{5134046535336719817}e^{12} + \frac{286637269758484976684}{1711348845112239939}e^{11} + \frac{1720703746215622483444}{5134046535336719817}e^{10} + \frac{1081509463974267668498}{1711348845112239939}e^{9} + \frac{5225412728378121513632}{5134046535336719817}e^{8} + \frac{8715322025347837508272}{5134046535336719817}e^{7} + \frac{2769450331061573491952}{5134046535336719817}e^{6} + \frac{1636617703171539545884}{5134046535336719817}e^{5} + \frac{788324140238080303885}{5134046535336719817}e^{4} + \frac{239150997140836206632}{5134046535336719817}e^{3} - \frac{16234970307545159764}{1711348845112239939}e^{2} + \frac{1597770222093685448}{570449615037413313}e - \frac{67702128054817180}{190149871679137771}$ |
| $2$ | $[2, 2, w + 1]$ | $\frac{153833952361360}{570449615037413313}e^{19} - \frac{48073110112925}{190149871679137771}e^{18} + \frac{788399005851970}{190149871679137771}e^{17} - \frac{4682377724306302}{570449615037413313}e^{16} + \frac{38400800358204490}{570449615037413313}e^{15} + \frac{79734060433297405}{570449615037413313}e^{14} + \frac{482894391084331625}{570449615037413313}e^{13} + \frac{611220751219773620}{570449615037413313}e^{12} + \frac{6079255763164326794}{570449615037413313}e^{11} + \frac{1403004104023693540}{570449615037413313}e^{10} + \frac{2478072680101057900}{570449615037413313}e^{9} - \frac{4221972822557525200}{570449615037413313}e^{8} - \frac{804388122275528855}{570449615037413313}e^{7} - \frac{134874678709027974800}{570449615037413313}e^{6} - \frac{294130516914920320}{570449615037413313}e^{5} - \frac{204397249578134515}{570449615037413313}e^{4} + \frac{14931508001074505}{190149871679137771}e^{3} - \frac{3836234187011415}{190149871679137771}e^{2} + \frac{2384979410865860708}{570449615037413313}e - \frac{259594794609795}{190149871679137771}$ |