Properties

Label 2.2.429.1-1.1-g
Base field \(\Q(\sqrt{429}) \)
Weight $[2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $8$
CM no
Base change no

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Base field \(\Q(\sqrt{429}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[1, 1, 1]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $52$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} + 72x^{6} + 1300x^{4} + 3024x^{2} + 1156\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 11]$ $-\frac{1}{342}e^{6} - \frac{37}{171}e^{4} - \frac{667}{171}e^{2} - \frac{794}{171}$
4 $[4, 2, 2]$ $-\frac{1}{684}e^{6} - \frac{37}{342}e^{4} - \frac{667}{342}e^{2} - \frac{226}{171}$
5 $[5, 5, w + 1]$ $-\frac{37}{23256}e^{7} - \frac{2681}{23256}e^{5} - \frac{24679}{11628}e^{3} - \frac{73097}{11628}e$
5 $[5, 5, w + 3]$ $\phantom{-}\frac{37}{23256}e^{7} + \frac{2681}{23256}e^{5} + \frac{24679}{11628}e^{3} + \frac{73097}{11628}e$
7 $[7, 7, w + 1]$ $\phantom{-}\frac{37}{23256}e^{7} + \frac{2681}{23256}e^{5} + \frac{24679}{11628}e^{3} + \frac{61469}{11628}e$
7 $[7, 7, w + 5]$ $-\frac{37}{23256}e^{7} - \frac{2681}{23256}e^{5} - \frac{24679}{11628}e^{3} - \frac{61469}{11628}e$
11 $[11, 11, w + 5]$ $\phantom{-}0$
13 $[13, 13, w + 6]$ $\phantom{-}0$
17 $[17, 17, w - 10]$ $-\frac{5}{684}e^{6} - \frac{683}{1368}e^{4} - \frac{1411}{171}e^{2} - \frac{7883}{684}$
17 $[17, 17, w + 9]$ $-\frac{5}{684}e^{6} - \frac{683}{1368}e^{4} - \frac{1411}{171}e^{2} - \frac{7883}{684}$
19 $[19, 19, w + 3]$ $-\frac{11}{3876}e^{7} - \frac{511}{2584}e^{5} - \frac{3184}{969}e^{3} - \frac{4271}{1292}e$
19 $[19, 19, w + 15]$ $\phantom{-}\frac{11}{3876}e^{7} + \frac{511}{2584}e^{5} + \frac{3184}{969}e^{3} + \frac{4271}{1292}e$
29 $[29, 29, -2w + 21]$ $\phantom{-}\frac{7}{1368}e^{6} + \frac{461}{1368}e^{4} + \frac{3301}{684}e^{2} - \frac{655}{684}$
29 $[29, 29, 5w - 54]$ $\phantom{-}\frac{7}{1368}e^{6} + \frac{461}{1368}e^{4} + \frac{3301}{684}e^{2} - \frac{655}{684}$
47 $[47, 47, w + 18]$ $\phantom{-}\frac{137}{23256}e^{7} + \frac{2449}{5814}e^{5} + \frac{85565}{11628}e^{3} + \frac{31726}{2907}e$
47 $[47, 47, w + 28]$ $-\frac{137}{23256}e^{7} - \frac{2449}{5814}e^{5} - \frac{85565}{11628}e^{3} - \frac{31726}{2907}e$
59 $[59, 59, w + 27]$ $\phantom{-}\frac{37}{11628}e^{7} + \frac{2681}{11628}e^{5} + \frac{24679}{5814}e^{3} + \frac{73097}{5814}e$
59 $[59, 59, w + 31]$ $-\frac{37}{11628}e^{7} - \frac{2681}{11628}e^{5} - \frac{24679}{5814}e^{3} - \frac{73097}{5814}e$
71 $[71, 71, w + 21]$ $-\frac{211}{23256}e^{7} - \frac{7579}{11628}e^{5} - \frac{134923}{11628}e^{3} - \frac{136549}{5814}e$
71 $[71, 71, w + 49]$ $\phantom{-}\frac{211}{23256}e^{7} + \frac{7579}{11628}e^{5} + \frac{134923}{11628}e^{3} + \frac{136549}{5814}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).