# Properties

 Label 4.4.9248.1-26.2-c Base field 4.4.9248.1 Weight $[2, 2, 2, 2]$ Level norm $26$ Level $[26, 26, -w^{3} + 4w - 3]$ Dimension $8$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.9248.1

Generator $$w$$, with minimal polynomial $$x^{4} - 5x^{2} + 2$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[26, 26, -w^{3} + 4w - 3]$ Dimension: $8$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{8} - 3x^{7} - 67x^{6} + 255x^{5} + 1318x^{4} - 6568x^{3} - 4288x^{2} + 52336x - 60832$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}\frac{1}{64}e^{7} + \frac{1}{64}e^{6} - \frac{63}{64}e^{5} + \frac{7}{64}e^{4} + \frac{673}{32}e^{3} - \frac{343}{16}e^{2} - \frac{1195}{8}e + 254$
2 $[2, 2, w + 1]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}e$
13 $[13, 13, w^{2} + w - 3]$ $\phantom{-}1$
19 $[19, 19, -w^{3} + 3w + 1]$ $-\frac{1}{8}e^{7} - \frac{3}{16}e^{6} + \frac{121}{16}e^{5} + \frac{37}{16}e^{4} - \frac{2495}{16}e^{3} + \frac{909}{8}e^{2} + \frac{4303}{4}e - \frac{3299}{2}$
19 $[19, 19, -w^{3} + 3w - 1]$ $\phantom{-}\frac{11}{64}e^{7} + \frac{13}{64}e^{6} - \frac{679}{64}e^{5} - \frac{33}{64}e^{4} + \frac{887}{4}e^{3} - \frac{1603}{8}e^{2} - \frac{6169}{4}e + \frac{10067}{4}$
43 $[43, 43, -w^{2} + w - 1]$ $-\frac{11}{64}e^{7} - \frac{13}{64}e^{6} + \frac{679}{64}e^{5} + \frac{33}{64}e^{4} - \frac{887}{4}e^{3} + \frac{1595}{8}e^{2} + \frac{6165}{4}e - \frac{9995}{4}$
43 $[43, 43, w^{2} + w + 1]$ $\phantom{-}\frac{3}{32}e^{7} + \frac{3}{32}e^{6} - \frac{189}{32}e^{5} + \frac{13}{32}e^{4} + \frac{2003}{16}e^{3} - \frac{963}{8}e^{2} - \frac{3517}{4}e + 1451$
49 $[49, 7, w^{3} + w^{2} - 6w - 3]$ $-\frac{1}{4}e^{7} - \frac{3}{8}e^{6} + \frac{121}{8}e^{5} + \frac{35}{8}e^{4} - \frac{2499}{8}e^{3} + 236e^{2} + \frac{4321}{2}e - 3370$
49 $[49, 7, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}\frac{3}{16}e^{7} + \frac{3}{16}e^{6} - \frac{189}{16}e^{5} + \frac{13}{16}e^{4} + \frac{2003}{8}e^{3} - \frac{967}{4}e^{2} - \frac{3515}{2}e + 2918$
53 $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ $\phantom{-}\frac{1}{32}e^{7} + \frac{3}{32}e^{6} - \frac{53}{32}e^{5} - \frac{87}{32}e^{4} + \frac{123}{4}e^{3} + \frac{31}{4}e^{2} - \frac{393}{2}e + \frac{369}{2}$
53 $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ $-e^{2} - 2e + 22$
59 $[59, 59, w^{3} - w^{2} - 4w + 1]$ $-\frac{3}{32}e^{7} - \frac{3}{32}e^{6} + \frac{189}{32}e^{5} - \frac{13}{32}e^{4} - \frac{2003}{16}e^{3} + \frac{963}{8}e^{2} + \frac{3509}{4}e - 1447$
59 $[59, 59, -w^{3} - w^{2} + 4w + 1]$ $-\frac{1}{16}e^{6} - \frac{5}{16}e^{5} + \frac{43}{16}e^{4} + \frac{173}{16}e^{3} - \frac{327}{8}e^{2} - \frac{369}{4}e + \frac{473}{2}$
67 $[67, 67, 3w^{3} - 13w + 1]$ $\phantom{-}\frac{3}{32}e^{7} + \frac{3}{32}e^{6} - \frac{189}{32}e^{5} + \frac{13}{32}e^{4} + \frac{2003}{16}e^{3} - \frac{971}{8}e^{2} - \frac{3513}{4}e + 1465$
67 $[67, 67, -w^{3} + w^{2} + 6w - 5]$ $\phantom{-}\frac{1}{16}e^{6} + \frac{5}{16}e^{5} - \frac{43}{16}e^{4} - \frac{173}{16}e^{3} + \frac{327}{8}e^{2} + \frac{369}{4}e - \frac{473}{2}$
81 $[81, 3, -3]$ $-\frac{3}{16}e^{7} - \frac{3}{16}e^{6} + \frac{189}{16}e^{5} - \frac{13}{16}e^{4} - \frac{2003}{8}e^{3} + \frac{967}{4}e^{2} + \frac{3515}{2}e - 2914$
83 $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ $\phantom{-}\frac{17}{64}e^{7} + \frac{15}{64}e^{6} - \frac{1077}{64}e^{5} + \frac{165}{64}e^{4} + \frac{1429}{4}e^{3} - \frac{2897}{8}e^{2} - \frac{10011}{4}e + \frac{16801}{4}$
83 $[83, 83, 4w^{3} - 18w - 1]$ $\phantom{-}\frac{1}{8}e^{7} + \frac{3}{16}e^{6} - \frac{121}{16}e^{5} - \frac{37}{16}e^{4} + \frac{2495}{16}e^{3} - \frac{917}{8}e^{2} - \frac{4315}{4}e + \frac{3343}{2}$
89 $[89, 89, -2w^{3} + 10w + 1]$ $\phantom{-}\frac{5}{32}e^{7} + \frac{7}{32}e^{6} - \frac{305}{32}e^{5} - \frac{67}{32}e^{4} + \frac{395}{2}e^{3} - 158e^{2} - \frac{2731}{2}e + \frac{4339}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,w+1]$ $-1$
$13$ $[13,13,w^{2}+w-3]$ $-1$