Properties

Label 2.2.29.1-45.1-c
Base field \(\Q(\sqrt{29}) \)
Weight $[2, 2]$
Level norm $45$
Level $[45, 15, 3w + 3]$
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: $[45, 15, 3w + 3]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 12x^{3} - 3x^{2} + 30x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $\phantom{-}1$
5 $[5, 5, w - 2]$ $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 4e^{2} + \frac{9}{2}e + 4$
7 $[7, 7, w]$ $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 3e^{2} + \frac{11}{2}e$
7 $[7, 7, -w + 1]$ $-e^{2} + e + 4$
9 $[9, 3, 3]$ $\phantom{-}1$
13 $[13, 13, w + 4]$ $\phantom{-}e^{4} - 2e^{3} - 7e^{2} + 10e + 4$
13 $[13, 13, w - 5]$ $-\frac{1}{2}e^{4} + 5e^{2} + \frac{1}{2}e - 5$
23 $[23, 23, -w - 5]$ $-e^{4} + 2e^{3} + 8e^{2} - 11e - 10$
23 $[23, 23, w - 6]$ $-\frac{1}{2}e^{4} + 2e^{3} + 2e^{2} - \frac{21}{2}e + 5$
29 $[29, 29, 2w - 1]$ $-\frac{1}{2}e^{4} + e^{3} + 4e^{2} - \frac{13}{2}e - 6$
53 $[53, 53, 3w - 5]$ $-\frac{1}{2}e^{4} + 2e^{3} + 4e^{2} - \frac{25}{2}e - 5$
53 $[53, 53, -3w - 2]$ $-2e^{3} + 2e^{2} + 14e - 8$
59 $[59, 59, -3w - 1]$ $\phantom{-}\frac{1}{2}e^{4} - 3e^{3} + \frac{37}{2}e - 6$
59 $[59, 59, 3w - 4]$ $-\frac{1}{2}e^{4} + 2e^{3} + 2e^{2} - \frac{25}{2}e + 3$
67 $[67, 67, 3w - 13]$ $\phantom{-}e^{4} - 4e^{3} - 5e^{2} + 24e - 4$
67 $[67, 67, -3w - 10]$ $-e^{4} + 2e^{3} + 7e^{2} - 12e - 8$
71 $[71, 71, 2w - 11]$ $\phantom{-}\frac{1}{2}e^{4} - 6e^{2} - \frac{7}{2}e + 11$
71 $[71, 71, -2w - 9]$ $-\frac{1}{2}e^{4} + 4e^{2} + \frac{7}{2}e - 9$
83 $[83, 83, -w - 9]$ $-\frac{1}{2}e^{4} + 3e^{3} + 2e^{2} - \frac{37}{2}e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w + 1]$ $-1$
$9$ $[9, 3, 3]$ $-1$