Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 29
Level $[29, 29, -w^{2} + 9]$
Label 4.4.17725.1-29.1-b
Dimension 29
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 $[29, 29, -w^{2} + 9]$
Label 4.4.17725.1-29.1-b
Dimension 29
Is CM no
Is base change no
Parent newspace dimension 52

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{29} - 5x^{28} - 144x^{27} + 604x^{26} + 9377x^{25} - 29883x^{24} - 362472x^{23} + 751116x^{22} + 9086052x^{21} - 8784522x^{20} - 150435338x^{19} - 7235931x^{18} + 1598132639x^{17} + 1545050122x^{16} - 9935841081x^{15} - 19040564543x^{14} + 26927303857x^{13} + 99852755298x^{12} + 26949391194x^{11} - 196373595187x^{10} - 245837785679x^{9} - 11867548014x^{8} + 157436008180x^{7} + 85073299192x^{6} - 16754876144x^{5} - 22444223799x^{4} - 2418319572x^{3} + 1259429276x^{2} + 171019952x + 4104048\)

  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 $[29, 29, -w^{2} + 9]$ $-1$
29 $[29, 29, -w^{2} + 2w + 6]$ $...$
29 $[29, 29, w^{2} - 7]$ $...$
29 $[29, 29, -w^{2} + 2w + 8]$ $...$
31 $[31, 31, -2w^{2} + w + 12]$ $...$
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
29 $[29, 29, -w^{2} + 9]$ $1$