Properties

Label 2.2.29.1-53.2-c
Base field \(\Q(\sqrt{29}) \)
Weight $[2, 2]$
Level norm $53$
Level $[53,53,-3w - 2]$
Dimension $5$
CM no
Base change no

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Base field \(\Q(\sqrt{29}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 7\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[53,53,-3w - 2]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{5} - x^{4} - 17x^{3} + 24x^{2} + 61x - 97\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $\phantom{-}\frac{5}{13}e^{4} + \frac{7}{13}e^{3} - \frac{76}{13}e^{2} - 4e + \frac{253}{13}$
5 $[5, 5, w - 2]$ $\phantom{-}\frac{5}{13}e^{4} + \frac{7}{13}e^{3} - \frac{63}{13}e^{2} - 3e + \frac{162}{13}$
7 $[7, 7, w]$ $\phantom{-}\frac{5}{13}e^{4} + \frac{7}{13}e^{3} - \frac{76}{13}e^{2} - 4e + \frac{227}{13}$
7 $[7, 7, -w + 1]$ $-\frac{14}{13}e^{4} - \frac{17}{13}e^{3} + \frac{192}{13}e^{2} + 7e - \frac{568}{13}$
9 $[9, 3, 3]$ $-\frac{14}{13}e^{4} - \frac{17}{13}e^{3} + \frac{205}{13}e^{2} + 8e - \frac{672}{13}$
13 $[13, 13, w + 4]$ $\phantom{-}\frac{6}{13}e^{4} - \frac{2}{13}e^{3} - \frac{99}{13}e^{2} + 2e + \frac{314}{13}$
13 $[13, 13, w - 5]$ $\phantom{-}e^{2} - 9$
23 $[23, 23, -w - 5]$ $\phantom{-}\frac{27}{13}e^{4} + \frac{30}{13}e^{3} - \frac{387}{13}e^{2} - 12e + \frac{1166}{13}$
23 $[23, 23, w - 6]$ $-\frac{1}{13}e^{4} - \frac{4}{13}e^{3} + \frac{10}{13}e^{2} + e - \frac{48}{13}$
29 $[29, 29, 2w - 1]$ $\phantom{-}\frac{4}{13}e^{4} + \frac{16}{13}e^{3} - \frac{40}{13}e^{2} - 8e + \frac{101}{13}$
53 $[53, 53, 3w - 5]$ $-\frac{5}{13}e^{4} - \frac{7}{13}e^{3} + \frac{50}{13}e^{2} + 3e - \frac{123}{13}$
53 $[53, 53, -3w - 2]$ $\phantom{-}1$
59 $[59, 59, -3w - 1]$ $-\frac{2}{13}e^{4} - \frac{8}{13}e^{3} + \frac{20}{13}e^{2} + 5e - \frac{44}{13}$
59 $[59, 59, 3w - 4]$ $\phantom{-}\frac{15}{13}e^{4} + \frac{21}{13}e^{3} - \frac{202}{13}e^{2} - 9e + \frac{512}{13}$
67 $[67, 67, 3w - 13]$ $\phantom{-}\frac{4}{13}e^{4} + \frac{3}{13}e^{3} - \frac{53}{13}e^{2} - 2e + \frac{88}{13}$
67 $[67, 67, -3w - 10]$ $-\frac{3}{13}e^{4} + \frac{1}{13}e^{3} + \frac{30}{13}e^{2} - 3e - \frac{66}{13}$
71 $[71, 71, 2w - 11]$ $-\frac{3}{13}e^{4} + \frac{14}{13}e^{3} + \frac{69}{13}e^{2} - 8e - \frac{170}{13}$
71 $[71, 71, -2w - 9]$ $\phantom{-}\frac{31}{13}e^{4} + \frac{33}{13}e^{3} - \frac{453}{13}e^{2} - 17e + \frac{1501}{13}$
83 $[83, 83, -w - 9]$ $-\frac{3}{13}e^{4} + \frac{14}{13}e^{3} + \frac{95}{13}e^{2} - 9e - \frac{378}{13}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53,53,-3w - 2]$ $-1$