Properties

Base field 3.3.733.1
Weight [2, 2, 2]
Level norm 11
Level $[11, 11, -w^{2} + 5]$
Label 3.3.733.1-11.1-b
Dimension 9
CM no
Base change no

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Base field 3.3.733.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 8\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[11, 11, -w^{2} + 5]$
Label 3.3.733.1-11.1-b
Dimension 9
Is CM no
Is base change no
Parent newspace dimension 13

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{9} \) \(\mathstrut -\mathstrut 2x^{8} \) \(\mathstrut -\mathstrut 13x^{7} \) \(\mathstrut +\mathstrut 25x^{6} \) \(\mathstrut +\mathstrut 47x^{5} \) \(\mathstrut -\mathstrut 85x^{4} \) \(\mathstrut -\mathstrut 36x^{3} \) \(\mathstrut +\mathstrut 41x^{2} \) \(\mathstrut +\mathstrut 23x \) \(\mathstrut +\mathstrut 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 5]$ $-e^{8} + 2e^{7} + 13e^{6} - 25e^{5} - 47e^{4} + 86e^{3} + 35e^{2} - 48e - 16$
5 $[5, 5, -w + 3]$ $\phantom{-}2e^{8} - 5e^{7} - 24e^{6} + 62e^{5} + 70e^{4} - 206e^{3} + 5e^{2} + 86e + 18$
7 $[7, 7, -w^{2} - 2w + 3]$ $-4e^{8} + 9e^{7} + 49e^{6} - 112e^{5} - 150e^{4} + 374e^{3} + 15e^{2} - 155e - 34$
11 $[11, 11, -w^{2} + 5]$ $\phantom{-}1$
13 $[13, 13, w + 1]$ $\phantom{-}4e^{8} - 9e^{7} - 50e^{6} + 113e^{5} + 162e^{4} - 385e^{3} - 52e^{2} + 186e + 47$
23 $[23, 23, w^{2} - 3]$ $\phantom{-}10e^{8} - 23e^{7} - 123e^{6} + 287e^{5} + 383e^{4} - 966e^{3} - 69e^{2} + 432e + 105$
25 $[25, 5, w^{2} + 2w - 1]$ $-6e^{8} + 14e^{7} + 74e^{6} - 175e^{5} - 232e^{4} + 590e^{3} + 46e^{2} - 266e - 61$
27 $[27, 3, -3]$ $-3e^{8} + 7e^{7} + 37e^{6} - 88e^{5} - 116e^{4} + 300e^{3} + 24e^{2} - 145e - 32$
29 $[29, 29, -3w + 7]$ $-e^{8} + 2e^{7} + 12e^{6} - 25e^{5} - 33e^{4} + 83e^{3} - 14e^{2} - 25e - 3$
43 $[43, 43, -3w^{2} - 2w + 17]$ $\phantom{-}9e^{8} - 20e^{7} - 112e^{6} + 250e^{5} + 358e^{4} - 844e^{3} - 95e^{2} + 382e + 92$
49 $[49, 7, -2w^{2} + w + 11]$ $-7e^{8} + 16e^{7} + 86e^{6} - 200e^{5} - 267e^{4} + 677e^{3} + 46e^{2} - 315e - 70$
67 $[67, 67, -2w^{2} - 4w + 3]$ $\phantom{-}e^{7} - 2e^{6} - 11e^{5} + 24e^{4} + 24e^{3} - 77e^{2} + 30e + 23$
71 $[71, 71, -2w^{2} + w + 9]$ $-3e^{8} + 7e^{7} + 38e^{6} - 88e^{5} - 130e^{4} + 303e^{3} + 73e^{2} - 164e - 48$
73 $[73, 73, w^{2} + 2w - 7]$ $-8e^{8} + 18e^{7} + 98e^{6} - 224e^{5} - 301e^{4} + 750e^{3} + 38e^{2} - 323e - 76$
73 $[73, 73, -2w^{2} - 2w + 11]$ $-15e^{8} + 34e^{7} + 185e^{6} - 423e^{5} - 582e^{4} + 1421e^{3} + 130e^{2} - 643e - 151$
73 $[73, 73, w - 5]$ $-8e^{8} + 20e^{7} + 96e^{6} - 249e^{5} - 278e^{4} + 831e^{3} - 33e^{2} - 350e - 67$
89 $[89, 89, 2w^{2} + w - 9]$ $\phantom{-}16e^{8} - 37e^{7} - 197e^{6} + 461e^{5} + 616e^{4} - 1548e^{3} - 121e^{2} + 689e + 165$
89 $[89, 89, -w^{2} - 2w + 9]$ $\phantom{-}4e^{8} - 9e^{7} - 50e^{6} + 113e^{5} + 162e^{4} - 382e^{3} - 53e^{2} + 166e + 51$
89 $[89, 89, -2w - 1]$ $\phantom{-}12e^{8} - 27e^{7} - 149e^{6} + 337e^{5} + 476e^{4} - 1136e^{3} - 131e^{2} + 521e + 129$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{2} + 5]$ $-1$