# Properties

 Base field $\Q(\sqrt{101})$ Weight [2, 2] Level norm 25 Level $[25,25,-w + 1]$ Label 2.2.101.1-25.3-c Dimension 4 CM no Base change no

# Related objects

• L-function not available

## 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 $[25,25,-w + 1]$ Label 2.2.101.1-25.3-c Dimension 4 Is CM no Is base change no Parent newspace dimension 30

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$x^{4}$ $\mathstrut +\mathstrut 3x^{3}$ $\mathstrut -\mathstrut 9x^{2}$ $\mathstrut -\mathstrut 27x$ $\mathstrut -\mathstrut 8$
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, -w + 5]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{2}e^{2} - \frac{7}{4}e - 3$
5 $[5, 5, -w - 4]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 6$
13 $[13, 13, w + 3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 4e + 3$
13 $[13, 13, w - 4]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 4e - 3$
17 $[17, 17, w + 6]$ $\phantom{-}\frac{3}{4}e^{3} + e^{2} - \frac{31}{4}e - 7$
17 $[17, 17, -w + 7]$ $-\frac{3}{4}e^{3} - e^{2} + \frac{31}{4}e + 7$
19 $[19, 19, w + 2]$ $\phantom{-}e^{2} - 7$
19 $[19, 19, w - 3]$ $\phantom{-}e^{2} - 7$
23 $[23, 23, w + 1]$ $-\frac{1}{2}e^{3} - e^{2} + \frac{13}{2}e + 9$
23 $[23, 23, -w + 2]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{13}{2}e - 9$
31 $[31, 31, -w - 7]$ $-e + 1$
31 $[31, 31, w - 8]$ $-e + 1$
37 $[37, 37, 2w - 9]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{13}{4}e - 4$
37 $[37, 37, 2w + 7]$ $-\frac{1}{4}e^{3} + \frac{13}{4}e + 4$
43 $[43, 43, 4w + 17]$ $-2e - 4$
43 $[43, 43, 4w - 21]$ $\phantom{-}2e + 4$
47 $[47, 47, -w - 8]$ $\phantom{-}e^{3} + e^{2} - 9e - 11$
47 $[47, 47, w - 9]$ $-e^{3} - e^{2} + 9e + 11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5,5,w + 4]$ $1$