Properties

Label 2.2.101.1-19.2-a
Base field \(\Q(\sqrt{101}) \)
Weight $[2, 2]$
Level norm $19$
Level $[19,19,-w + 3]$
Dimension $12$
CM no
Base change no

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Base field \(\Q(\sqrt{101}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[19,19,-w + 3]$
Dimension: $12$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} + 8x^{11} - 150x^{9} - 319x^{8} + 596x^{7} + 2387x^{6} + 844x^{5} - 3610x^{4} - 3169x^{3} + 420x^{2} + 754x - 7\)

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Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, -w + 5]$ $...$
5 $[5, 5, -w - 4]$ $...$
9 $[9, 3, 3]$ $...$
13 $[13, 13, w + 3]$ $...$
13 $[13, 13, w - 4]$ $...$
17 $[17, 17, w + 6]$ $...$
17 $[17, 17, -w + 7]$ $...$
19 $[19, 19, w + 2]$ $...$
19 $[19, 19, w - 3]$ $\phantom{-}1$
23 $[23, 23, w + 1]$ $...$
23 $[23, 23, -w + 2]$ $...$
31 $[31, 31, -w - 7]$ $...$
31 $[31, 31, w - 8]$ $...$
37 $[37, 37, 2w - 9]$ $...$
37 $[37, 37, 2w + 7]$ $...$
43 $[43, 43, 4w + 17]$ $...$
43 $[43, 43, 4w - 21]$ $...$
47 $[47, 47, -w - 8]$ $...$
47 $[47, 47, w - 9]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-w + 3]$ $-1$