Properties

Base field 4.4.11525.1
Weight [2, 2, 2, 2]
Level norm 25
Level $[25, 5, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{12}{5}w + 1]$
Label 4.4.11525.1-25.2-c
Dimension 7
CM no
Base change yes

Related objects

Downloads

Learn more about

Base field 4.4.11525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[25, 5, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{12}{5}w + 1]$
Label 4.4.11525.1-25.2-c
Dimension 7
Is CM no
Is base change yes
Parent newspace dimension 23

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} \) \(\mathstrut -\mathstrut 4x^{6} \) \(\mathstrut -\mathstrut 29x^{5} \) \(\mathstrut +\mathstrut 81x^{4} \) \(\mathstrut +\mathstrut 207x^{3} \) \(\mathstrut -\mathstrut 429x^{2} \) \(\mathstrut -\mathstrut 197x \) \(\mathstrut -\mathstrut 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}1$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}1$
11 $[11, 11, w + 1]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-\frac{314}{9127}e^{6} + \frac{2016}{9127}e^{5} + \frac{7482}{9127}e^{4} - \frac{48194}{9127}e^{3} - \frac{53049}{9127}e^{2} + \frac{255780}{9127}e + \frac{74861}{9127}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $-\frac{157}{9127}e^{6} + \frac{1008}{9127}e^{5} + \frac{3741}{9127}e^{4} - \frac{24097}{9127}e^{3} - \frac{31088}{9127}e^{2} + \frac{137017}{9127}e + \frac{60248}{9127}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $\phantom{-}\frac{59}{9127}e^{6} - \frac{30}{9127}e^{5} - \frac{3208}{9127}e^{4} + \frac{5335}{9127}e^{3} + \frac{27437}{9127}e^{2} - \frac{69977}{9127}e + \frac{380}{9127}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $-\frac{157}{9127}e^{6} + \frac{1008}{9127}e^{5} + \frac{3741}{9127}e^{4} - \frac{24097}{9127}e^{3} - \frac{31088}{9127}e^{2} + \frac{137017}{9127}e + \frac{60248}{9127}$
19 $[19, 19, w - 1]$ $\phantom{-}\frac{59}{9127}e^{6} - \frac{30}{9127}e^{5} - \frac{3208}{9127}e^{4} + \frac{5335}{9127}e^{3} + \frac{27437}{9127}e^{2} - \frac{69977}{9127}e + \frac{380}{9127}$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}\frac{655}{9127}e^{6} - \frac{1880}{9127}e^{5} - \frac{21537}{9127}e^{4} + \frac{36178}{9127}e^{3} + \frac{155626}{9127}e^{2} - \frac{211144}{9127}e - \frac{79626}{9127}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}\frac{655}{9127}e^{6} - \frac{1880}{9127}e^{5} - \frac{21537}{9127}e^{4} + \frac{36178}{9127}e^{3} + \frac{155626}{9127}e^{2} - \frac{211144}{9127}e - \frac{79626}{9127}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $\phantom{-}\frac{445}{9127}e^{6} - \frac{2392}{9127}e^{5} - \frac{9964}{9127}e^{4} + \frac{48128}{9127}e^{3} + \frac{51317}{9127}e^{2} - \frac{239596}{9127}e + \frac{5960}{9127}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}\frac{445}{9127}e^{6} - \frac{2392}{9127}e^{5} - \frac{9964}{9127}e^{4} + \frac{48128}{9127}e^{3} + \frac{51317}{9127}e^{2} - \frac{239596}{9127}e + \frac{5960}{9127}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $\phantom{-}\frac{625}{9127}e^{6} - \frac{3257}{9127}e^{5} - \frac{17276}{9127}e^{4} + \frac{75697}{9127}e^{3} + \frac{138117}{9127}e^{2} - \frac{430345}{9127}e - \frac{153454}{9127}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $\phantom{-}\frac{625}{9127}e^{6} - \frac{3257}{9127}e^{5} - \frac{17276}{9127}e^{4} + \frac{75697}{9127}e^{3} + \frac{138117}{9127}e^{2} - \frac{430345}{9127}e - \frac{153454}{9127}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $\phantom{-}\frac{1640}{9127}e^{6} - \frac{6867}{9127}e^{5} - \frac{44310}{9127}e^{4} + \frac{130505}{9127}e^{3} + \frac{284803}{9127}e^{2} - \frac{630526}{9127}e - \frac{168574}{9127}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $\phantom{-}\frac{1640}{9127}e^{6} - \frac{6867}{9127}e^{5} - \frac{44310}{9127}e^{4} + \frac{130505}{9127}e^{3} + \frac{284803}{9127}e^{2} - \frac{630526}{9127}e - \frac{168574}{9127}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $-\frac{1539}{9127}e^{6} + \frac{5114}{9127}e^{5} + \frac{46089}{9127}e^{4} - \frac{91052}{9127}e^{3} - \frac{313171}{9127}e^{2} + \frac{473144}{9127}e + \frac{166440}{9127}$
71 $[71, 71, w^{2} - 8]$ $-\frac{1539}{9127}e^{6} + \frac{5114}{9127}e^{5} + \frac{46089}{9127}e^{4} - \frac{91052}{9127}e^{3} - \frac{313171}{9127}e^{2} + \frac{473144}{9127}e + \frac{166440}{9127}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $-\frac{285}{9127}e^{6} + \frac{609}{9127}e^{5} + \frac{8535}{9127}e^{4} - \frac{3340}{9127}e^{3} - \frac{52248}{9127}e^{2} - \frac{24271}{9127}e + \frac{47048}{9127}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $-1$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $-1$