Properties

Label 2.2.401.1-2.2-c
Base field \(\Q(\sqrt{401}) \)
Weight $[2, 2]$
Level norm $2$
Level $[2,2,-w + 1]$
Dimension $24$
CM no
Base change no

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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 $[83, 83, -4w - 37]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-w + 1]$ $\frac{342807969571301}{3640107823531103953}e^{23} + \frac{105760394851458}{3640107823531103953}e^{22} + \frac{2550220171817797}{3640107823531103953}e^{21} - \frac{1335802258417905}{3640107823531103953}e^{20} + \frac{299151360714048}{74287914765940897}e^{19} + \frac{6796259916042672}{3640107823531103953}e^{18} + \frac{86177144471765814}{3640107823531103953}e^{17} + \frac{6940046256044301}{520015403361586279}e^{16} + \frac{48547004671890073}{520015403361586279}e^{15} + \frac{186732938389730858}{3640107823531103953}e^{14} + \frac{935374107964921025}{3640107823531103953}e^{13} + \frac{350501734203943774}{3640107823531103953}e^{12} + \frac{2364233522745725476}{3640107823531103953}e^{11} + \frac{1516066500075478276}{3640107823531103953}e^{10} + \frac{5339252519428846644}{3640107823531103953}e^{9} + \frac{2354868064960612077}{3640107823531103953}e^{8} + \frac{6555513862351126555}{3640107823531103953}e^{7} + \frac{209146712383218574}{520015403361586279}e^{6} + \frac{4946934083996715001}{3640107823531103953}e^{5} - \frac{719827648060614039}{520015403361586279}e^{4} + \frac{3749857890628423873}{3640107823531103953}e^{3} + \frac{218483374914058335}{520015403361586279}e^{2} + \frac{44882845693573943}{74287914765940897}e + \frac{1669235857889273}{10612559252277271}$