Properties

Base field \(\Q(\sqrt{157}) \)
Weight [2, 2]
Level norm 13
Level $[13, 13, 2w - 13]$
Label 2.2.157.1-13.1-a
Dimension 21
CM no
Base change no

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{157}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[13, 13, 2w - 13]$
Label 2.2.157.1-13.1-a
Dimension 21
Is CM no
Is base change no
Parent newspace dimension 44

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{21} \) \(\mathstrut -\mathstrut 39x^{19} \) \(\mathstrut -\mathstrut 8x^{18} \) \(\mathstrut +\mathstrut 623x^{17} \) \(\mathstrut +\mathstrut 245x^{16} \) \(\mathstrut -\mathstrut 5224x^{15} \) \(\mathstrut -\mathstrut 2945x^{14} \) \(\mathstrut +\mathstrut 24469x^{13} \) \(\mathstrut +\mathstrut 17581x^{12} \) \(\mathstrut -\mathstrut 62802x^{11} \) \(\mathstrut -\mathstrut 54375x^{10} \) \(\mathstrut +\mathstrut 79882x^{9} \) \(\mathstrut +\mathstrut 83045x^{8} \) \(\mathstrut -\mathstrut 38167x^{7} \) \(\mathstrut -\mathstrut 55284x^{6} \) \(\mathstrut -\mathstrut 584x^{5} \) \(\mathstrut +\mathstrut 12950x^{4} \) \(\mathstrut +\mathstrut 3074x^{3} \) \(\mathstrut -\mathstrut 259x^{2} \) \(\mathstrut -\mathstrut 73x \) \(\mathstrut +\mathstrut 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}e$
3 $[3, 3, -w + 7]$ $...$
4 $[4, 2, 2]$ $...$
11 $[11, 11, -3w - 17]$ $...$
11 $[11, 11, 3w - 20]$ $...$
13 $[13, 13, 2w - 13]$ $\phantom{-}1$
13 $[13, 13, 2w + 11]$ $...$
17 $[17, 17, w + 7]$ $...$
17 $[17, 17, -w + 8]$ $...$
19 $[19, 19, -w - 4]$ $...$
19 $[19, 19, -w + 5]$ $...$
25 $[25, 5, 5]$ $...$
31 $[31, 31, -6w - 35]$ $...$
31 $[31, 31, -6w + 41]$ $...$
37 $[37, 37, -w - 1]$ $...$
37 $[37, 37, w - 2]$ $...$
47 $[47, 47, 3w + 16]$ $...$
47 $[47, 47, -3w + 19]$ $...$
49 $[49, 7, -7]$ $...$
67 $[67, 67, 3w - 22]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, 2w - 13]$ $-1$