# Properties

 Base field 4.4.19225.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ Label 4.4.19225.1-25.1-g Dimension 25 CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.19225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 15x^{2} + 2x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ Label 4.4.19225.1-25.1-g Dimension 25 Is CM no Is base change yes Parent newspace dimension 63

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{25} - 3x^{24} - 59x^{23} + 175x^{22} + 1473x^{21} - 4321x^{20} - 20413x^{19} + 59221x^{18} + 173547x^{17} - 497585x^{16} - 946745x^{15} + 2677975x^{14} + 3372140x^{13} - 9383966x^{12} - 7809644x^{11} + 21327922x^{10} + 11401243x^{9} - 30665177x^{8} - 9655767x^{7} + 26391167x^{6} + 3679560x^{5} - 12125976x^{4} + 181360x^{3} + 2222960x^{2} - 363648x - 2304$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}e$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $...$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $...$
11 $[11, 11, -w - 3]$ $...$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $-1$
29 $[29, 29, w + 1]$ $...$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $...$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $...$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $...$
31 $[31, 31, -w + 3]$ $...$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $...$
59 $[59, 59, 2w^{2} - w - 13]$ $...$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $...$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $...$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $...$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $...$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $...$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $1$