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: | $[2,2,-w + 1]$ |
Dimension: | $24$ |
CM: | no |
Base change: | no |
Newspace dimension: | $90$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{24} - x^{23} + 8x^{22} - 11x^{21} + 49x^{20} - 17x^{19} + 214x^{18} - 14x^{17} + 847x^{16} - 75x^{15} + 2299x^{14} - x^{13} + 5476x^{12} + 2124x^{11} + 10172x^{10} + 3293x^{9} + 15839x^{8} + 1729x^{7} + 11868x^{6} + 1841x^{5} + 8754x^{4} + 2933x^{3} + 5243x^{2} + 1029x + 2401\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $...$ |
5 | $[5, 5, w]$ | $...$ |
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 |
---|---|---|
$2$ | $[2,2,-w + 1]$ | $\frac{342807969571301}{3640107823531103953}e^{23} + \frac{105760394851458}{3640107823531103953}e^{22} + \frac{2550220171817797}{3640107823531103953}e^{21} - \frac{1335802258417905}{3640107823531103953}e^{20} + \frac{299151360714048}{74287914765940897}e^{19} + \frac{6796259916042672}{3640107823531103953}e^{18} + \frac{86177144471765814}{3640107823531103953}e^{17} + \frac{6940046256044301}{520015403361586279}e^{16} + \frac{48547004671890073}{520015403361586279}e^{15} + \frac{186732938389730858}{3640107823531103953}e^{14} + \frac{935374107964921025}{3640107823531103953}e^{13} + \frac{350501734203943774}{3640107823531103953}e^{12} + \frac{2364233522745725476}{3640107823531103953}e^{11} + \frac{1516066500075478276}{3640107823531103953}e^{10} + \frac{5339252519428846644}{3640107823531103953}e^{9} + \frac{2354868064960612077}{3640107823531103953}e^{8} + \frac{6555513862351126555}{3640107823531103953}e^{7} + \frac{209146712383218574}{520015403361586279}e^{6} + \frac{4946934083996715001}{3640107823531103953}e^{5} - \frac{719827648060614039}{520015403361586279}e^{4} + \frac{3749857890628423873}{3640107823531103953}e^{3} + \frac{218483374914058335}{520015403361586279}e^{2} + \frac{44882845693573943}{74287914765940897}e + \frac{1669235857889273}{10612559252277271}$ |