Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 31
Level $[31, 31, -2w^{2} + w + 12]$
Label 4.4.17725.1-31.1-b
Dimension 33
CM no
Base change no

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Base field 4.4.17725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[31, 31, -2w^{2} + w + 12]$
Label 4.4.17725.1-31.1-b
Dimension 33
Is CM no
Is base change no
Parent newspace dimension 59

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{33} - 14x^{32} - 81x^{31} + 1973x^{30} - 637x^{29} - 116866x^{28} + 313439x^{27} + 3761516x^{26} - 16528202x^{25} - 69577575x^{24} + 454590453x^{23} + 661153716x^{22} - 7733535779x^{21} - 175319215x^{20} + 85663905890x^{19} - 77230371437x^{18} - 620521532016x^{17} + 1015547163823x^{16} + 2826119182089x^{15} - 6857289879369x^{14} - 7065850709040x^{13} + 27261526134530x^{12} + 4123593429018x^{11} - 62635914256836x^{10} + 23660591791338x^{9} + 73472868519262x^{8} - 54443637858924x^{7} - 30646182875952x^{6} + 33343730036440x^{5} + 1404674931980x^{4} - 5319225952360x^{3} + 292439972480x^{2} + 247333072992x - 15579258048\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, w + 1]$ $...$
19 $[19, 19, -w^{2} + 6]$ $...$
19 $[19, 19, -w^{2} + 2w + 5]$ $...$
19 $[19, 19, -w + 2]$ $...$
25 $[25, 5, 2w^{2} - 2w - 13]$ $...$
29 $[29, 29, -w^{2} + 9]$ $...$
29 $[29, 29, -w^{2} + 2w + 6]$ $...$
29 $[29, 29, w^{2} - 7]$ $...$
29 $[29, 29, -w^{2} + 2w + 8]$ $...$
31 $[31, 31, -2w^{2} + w + 12]$ $-1$
31 $[31, 31, 2w^{2} - 3w - 11]$ $...$
41 $[41, 41, -w]$ $...$
41 $[41, 41, -w + 1]$ $...$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $...$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $...$
61 $[61, 61, 2w^{2} - 3w - 14]$ $...$
61 $[61, 61, 2w^{2} - w - 15]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, -2w^{2} + w + 12]$ $1$