Properties

Base field 4.4.18688.1
Weight [2, 2, 2, 2]
Level norm 28
Level $[28, 14, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - 4w + \frac{28}{3}]$
Label 4.4.18688.1-28.1-a
Dimension 10
CM no
Base change no

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Base field 4.4.18688.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[28, 14, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - 4w + \frac{28}{3}]$
Label 4.4.18688.1-28.1-a
Dimension 10
Is CM no
Is base change no
Parent newspace dimension 20

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} \) \(\mathstrut -\mathstrut 4x^{9} \) \(\mathstrut -\mathstrut 34x^{8} \) \(\mathstrut +\mathstrut 139x^{7} \) \(\mathstrut +\mathstrut 352x^{6} \) \(\mathstrut -\mathstrut 1461x^{5} \) \(\mathstrut -\mathstrut 1422x^{4} \) \(\mathstrut +\mathstrut 5424x^{3} \) \(\mathstrut +\mathstrut 3280x^{2} \) \(\mathstrut -\mathstrut 6656x \) \(\mathstrut -\mathstrut 4096\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $\phantom{-}1$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $...$
9 $[9, 3, w + 1]$ $...$
17 $[17, 17, w + 3]$ $...$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $...$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $-\frac{99175}{7791248}e^{9} + \frac{21609}{486953}e^{8} + \frac{1593891}{3895624}e^{7} - \frac{11167717}{7791248}e^{6} - \frac{7090681}{1947812}e^{5} + \frac{99289755}{7791248}e^{4} + \frac{33730791}{3895624}e^{3} - \frac{15144010}{486953}e^{2} - \frac{1611541}{486953}e + \frac{8196024}{486953}$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $...$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $...$
41 $[41, 41, w^{2} - 5]$ $...$
41 $[41, 41, 2w + 3]$ $-\frac{54747}{31164992}e^{9} + \frac{12171}{7791248}e^{8} + \frac{754739}{15582496}e^{7} - \frac{1781129}{31164992}e^{6} - \frac{145512}{486953}e^{5} + \frac{18017863}{31164992}e^{4} - \frac{723539}{15582496}e^{3} - \frac{2777525}{973906}e^{2} + \frac{498625}{1947812}e + \frac{3389625}{486953}$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $...$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $-\frac{8129}{3895624}e^{9} + \frac{72005}{1947812}e^{8} - \frac{82637}{1947812}e^{7} - \frac{4732655}{3895624}e^{6} + \frac{5505149}{1947812}e^{5} + \frac{44285417}{3895624}e^{4} - \frac{13143158}{486953}e^{3} - \frac{16026271}{486953}e^{2} + \frac{26218601}{486953}e + \frac{17446240}{486953}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $...$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $...$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $...$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $...$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $\phantom{-}\frac{11463}{1947812}e^{9} - \frac{21027}{973906}e^{8} - \frac{86072}{486953}e^{7} + \frac{1236637}{1947812}e^{6} + \frac{1340715}{973906}e^{5} - \frac{8295885}{1947812}e^{4} - \frac{1394624}{486953}e^{3} - \frac{175797}{973906}e^{2} + \frac{2423842}{486953}e + \frac{8236686}{486953}$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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