Properties

 Label 4.4.13525.1-29.1-a Base field 4.4.13525.1 Weight $[2, 2, 2, 2]$ Level norm $29$ Level $[29, 29, -w]$ Dimension $15$ CM no Base change no

Related objects

• L-function not available

Base field 4.4.13525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 12x^{2} + 8x + 29$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[29, 29, -w]$ Dimension: $15$ CM: no Base change: no Newspace dimension: $38$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{15} + 3x^{14} - 23x^{13} - 76x^{12} + 149x^{11} + 658x^{10} - 88x^{9} - 2176x^{8} - 1476x^{7} + 2192x^{6} + 2629x^{5} - 210x^{4} - 1182x^{3} - 395x^{2} - 10x + 1$$
Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $...$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $\phantom{-}e$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $...$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $...$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $...$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $...$
16 $[16, 2, 2]$ $...$
29 $[29, 29, -w]$ $\phantom{-}1$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $...$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $...$
41 $[41, 41, -w^{2} + 10]$ $...$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $...$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $...$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $...$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $...$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $...$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $...$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $...$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $...$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $...$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, -w]$ $-1$