# Properties

 Label 4.4.13525.1-25.1-i Base field 4.4.13525.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, \frac{2}{5}w^{3} - \frac{14}{5}w - \frac{3}{5}]$ Dimension $8$ CM no Base change yes

# 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: $[25, 5, \frac{2}{5}w^{3} - \frac{14}{5}w - \frac{3}{5}]$ Dimension: $8$ CM: no Base change: yes Newspace dimension: $27$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{8} - x^{7} - 38x^{6} + 24x^{5} + 367x^{4} - 275x^{3} - 738x^{2} + 796x - 200$$
Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $\phantom{-}1$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $\phantom{-}1$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $\phantom{-}e$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $\phantom{-}\frac{113}{1440}e^{7} - \frac{61}{1440}e^{6} - \frac{121}{40}e^{5} + \frac{67}{120}e^{4} + \frac{42683}{1440}e^{3} - \frac{1443}{160}e^{2} - \frac{257}{4}e + \frac{2521}{72}$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $\phantom{-}\frac{113}{1440}e^{7} - \frac{61}{1440}e^{6} - \frac{121}{40}e^{5} + \frac{67}{120}e^{4} + \frac{42683}{1440}e^{3} - \frac{1443}{160}e^{2} - \frac{257}{4}e + \frac{2521}{72}$
16 $[16, 2, 2]$ $-\frac{37}{480}e^{7} + \frac{17}{480}e^{6} + \frac{119}{40}e^{5} - \frac{11}{40}e^{4} - \frac{14023}{480}e^{3} + \frac{957}{160}e^{2} + \frac{1277}{20}e - \frac{653}{24}$
29 $[29, 29, -w]$ $-\frac{23}{720}e^{7} - \frac{1}{360}e^{6} + \frac{49}{40}e^{5} + \frac{67}{120}e^{4} - \frac{8447}{720}e^{3} - \frac{19}{5}e^{2} + \frac{517}{20}e - \frac{25}{9}$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $-\frac{23}{720}e^{7} - \frac{1}{360}e^{6} + \frac{49}{40}e^{5} + \frac{67}{120}e^{4} - \frac{8447}{720}e^{3} - \frac{19}{5}e^{2} + \frac{517}{20}e - \frac{25}{9}$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $\phantom{-}\frac{1}{16}e^{7} - \frac{19}{8}e^{5} - \frac{7}{8}e^{4} + \frac{353}{16}e^{3} + \frac{39}{8}e^{2} - \frac{165}{4}e + \frac{21}{2}$
41 $[41, 41, -w^{2} + 10]$ $-\frac{1}{288}e^{7} + \frac{43}{1440}e^{6} + \frac{1}{10}e^{5} - \frac{59}{60}e^{4} - \frac{1211}{1440}e^{3} + \frac{1217}{160}e^{2} + \frac{11}{5}e - \frac{451}{72}$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $-\frac{1}{288}e^{7} + \frac{43}{1440}e^{6} + \frac{1}{10}e^{5} - \frac{59}{60}e^{4} - \frac{1211}{1440}e^{3} + \frac{1217}{160}e^{2} + \frac{11}{5}e - \frac{451}{72}$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $\phantom{-}\frac{1}{16}e^{7} - \frac{19}{8}e^{5} - \frac{7}{8}e^{4} + \frac{353}{16}e^{3} + \frac{39}{8}e^{2} - \frac{165}{4}e + \frac{21}{2}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $-\frac{59}{720}e^{7} + \frac{43}{720}e^{6} + \frac{63}{20}e^{5} - \frac{61}{60}e^{4} - \frac{22649}{720}e^{3} + \frac{949}{80}e^{2} + \frac{149}{2}e - \frac{1495}{36}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $-\frac{59}{720}e^{7} + \frac{43}{720}e^{6} + \frac{63}{20}e^{5} - \frac{61}{60}e^{4} - \frac{22649}{720}e^{3} + \frac{949}{80}e^{2} + \frac{149}{2}e - \frac{1495}{36}$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $\phantom{-}\frac{83}{720}e^{7} - \frac{11}{144}e^{6} - \frac{22}{5}e^{5} + \frac{19}{15}e^{4} + \frac{30701}{720}e^{3} - \frac{1349}{80}e^{2} - \frac{917}{10}e + \frac{1975}{36}$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $\phantom{-}\frac{83}{720}e^{7} - \frac{11}{144}e^{6} - \frac{22}{5}e^{5} + \frac{19}{15}e^{4} + \frac{30701}{720}e^{3} - \frac{1349}{80}e^{2} - \frac{917}{10}e + \frac{1975}{36}$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $\phantom{-}\frac{31}{480}e^{7} - \frac{11}{480}e^{6} - \frac{97}{40}e^{5} - \frac{7}{40}e^{4} + \frac{10789}{480}e^{3} - \frac{111}{160}e^{2} - \frac{861}{20}e + \frac{527}{24}$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $\phantom{-}\frac{31}{480}e^{7} - \frac{11}{480}e^{6} - \frac{97}{40}e^{5} - \frac{7}{40}e^{4} + \frac{10789}{480}e^{3} - \frac{111}{160}e^{2} - \frac{861}{20}e + \frac{527}{24}$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $-\frac{13}{45}e^{7} + \frac{13}{90}e^{6} + 11e^{5} - \frac{4}{3}e^{4} - \frac{4729}{45}e^{3} + \frac{49}{2}e^{2} + \frac{1077}{5}e - \frac{968}{9}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 2]$ $-1$
$5$ $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $-1$