Properties

Base field 6.6.1241125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 45
Level $[45, 15, 2w^{5} - 14w^{3} - 3w^{2} + 23w + 9]$
Label 6.6.1241125.1-45.1-l
Dimension 7
CM no
Base change no

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Base field 6.6.1241125.1

Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[45, 15, 2w^{5} - 14w^{3} - 3w^{2} + 23w + 9]$
Label 6.6.1241125.1-45.1-l
Dimension 7
Is CM no
Is base change no
Parent newspace dimension 27

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} \) \(\mathstrut -\mathstrut 74x^{5} \) \(\mathstrut -\mathstrut 40x^{4} \) \(\mathstrut +\mathstrut 1744x^{3} \) \(\mathstrut +\mathstrut 2112x^{2} \) \(\mathstrut -\mathstrut 13248x \) \(\mathstrut -\mathstrut 24192\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $-1$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $-1$
11 $[11, 11, w - 1]$ $\phantom{-}e$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $-\frac{1}{96}e^{6} + \frac{1}{16}e^{5} + \frac{37}{48}e^{4} - \frac{77}{24}e^{3} - \frac{109}{6}e^{2} + 37e + 142$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $\phantom{-}\frac{1}{2}e^{2} - 12$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}\frac{1}{120}e^{6} + \frac{1}{40}e^{5} - \frac{5}{12}e^{4} - \frac{13}{12}e^{3} + \frac{151}{30}e^{2} + \frac{51}{5}e - \frac{54}{5}$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $\phantom{-}\frac{1}{480}e^{6} + \frac{3}{80}e^{5} - \frac{5}{48}e^{4} - \frac{47}{24}e^{3} + \frac{19}{30}e^{2} + \frac{114}{5}e + \frac{104}{5}$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $-\frac{1}{40}e^{6} + \frac{1}{20}e^{5} + \frac{3}{2}e^{4} - \frac{5}{2}e^{3} - \frac{261}{10}e^{2} + \frac{127}{5}e + \frac{732}{5}$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $-\frac{3}{160}e^{6} + \frac{3}{80}e^{5} + \frac{19}{16}e^{4} - \frac{17}{8}e^{3} - \frac{227}{10}e^{2} + \frac{129}{5}e + \frac{714}{5}$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $-\frac{1}{48}e^{6} + \frac{1}{8}e^{5} + \frac{37}{24}e^{4} - \frac{77}{12}e^{3} - \frac{215}{6}e^{2} + 73e + 280$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $\phantom{-}\frac{1}{80}e^{6} - \frac{1}{40}e^{5} - \frac{7}{8}e^{4} + \frac{5}{4}e^{3} + \frac{183}{10}e^{2} - \frac{66}{5}e - \frac{556}{5}$
64 $[64, 2, 2]$ $-\frac{1}{96}e^{6} + \frac{1}{8}e^{5} + \frac{49}{48}e^{4} - \frac{19}{3}e^{3} - \frac{89}{3}e^{2} + 72e + 257$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}\frac{1}{8}e^{5} + \frac{1}{4}e^{4} - \frac{25}{4}e^{3} - \frac{25}{2}e^{2} + 69e + 156$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $\phantom{-}\frac{1}{60}e^{6} - \frac{3}{40}e^{5} - \frac{13}{12}e^{4} + \frac{43}{12}e^{3} + \frac{316}{15}e^{2} - \frac{178}{5}e - \frac{648}{5}$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $\phantom{-}\frac{1}{30}e^{6} - \frac{1}{40}e^{5} - \frac{23}{12}e^{4} + \frac{17}{12}e^{3} + \frac{919}{30}e^{2} - \frac{71}{5}e - \frac{706}{5}$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $\phantom{-}\frac{17}{480}e^{6} - \frac{9}{80}e^{5} - \frac{109}{48}e^{4} + \frac{137}{24}e^{3} + \frac{664}{15}e^{2} - \frac{302}{5}e - \frac{1412}{5}$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $-\frac{7}{240}e^{6} - \frac{1}{40}e^{5} + \frac{41}{24}e^{4} + \frac{11}{12}e^{3} - \frac{418}{15}e^{2} - \frac{36}{5}e + \frac{594}{5}$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $-\frac{1}{120}e^{6} - \frac{1}{40}e^{5} + \frac{5}{12}e^{4} + \frac{13}{12}e^{3} - \frac{83}{15}e^{2} - \frac{46}{5}e + \frac{114}{5}$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $-\frac{1}{240}e^{6} + \frac{1}{20}e^{5} + \frac{11}{24}e^{4} - \frac{7}{3}e^{3} - \frac{413}{30}e^{2} + \frac{117}{5}e + \frac{582}{5}$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $-\frac{3}{160}e^{6} + \frac{3}{80}e^{5} + \frac{19}{16}e^{4} - \frac{17}{8}e^{3} - \frac{116}{5}e^{2} + \frac{139}{5}e + \frac{744}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $1$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $1$