Properties

Label 2.2.193.1-8.3-c
Base field \(\Q(\sqrt{193}) \)
Weight $[2, 2]$
Level norm $8$
Level $[8, 8, -w + 8]$
Dimension $14$
CM no
Base change no

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Base field \(\Q(\sqrt{193}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 48\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[8, 8, -w + 8]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} - 2x^{13} - 21x^{12} + 40x^{11} + 169x^{10} - 307x^{9} - 645x^{8} + 1130x^{7} + 1149x^{6} - 2017x^{5} - 738x^{4} + 1537x^{3} - 39x^{2} - 377x + 88\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -9w - 58]$ $\phantom{-}0$
2 $[2, 2, -9w + 67]$ $\phantom{-}e$
3 $[3, 3, -2w + 15]$ $...$
3 $[3, 3, 2w + 13]$ $...$
7 $[7, 7, 186w - 1385]$ $...$
7 $[7, 7, -186w - 1199]$ $...$
23 $[23, 23, -38w - 245]$ $...$
23 $[23, 23, 38w - 283]$ $...$
25 $[25, 5, 5]$ $...$
31 $[31, 31, 16w - 119]$ $...$
31 $[31, 31, 16w + 103]$ $...$
43 $[43, 43, 4w + 25]$ $...$
43 $[43, 43, -4w + 29]$ $...$
59 $[59, 59, 12w - 89]$ $...$
59 $[59, 59, -12w - 77]$ $...$
67 $[67, 67, 92w + 593]$ $...$
67 $[67, 67, 92w - 685]$ $...$
83 $[83, 83, 204w - 1519]$ $...$
83 $[83, 83, 204w + 1315]$ $...$
97 $[97, 97, -24w + 179]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -9w - 58]$ $1$