Properties

Base field \(\Q(\sqrt{197}) \)
Weight [2, 2]
Level norm 28
Level $[28,14,-2w - 12]$
Label 2.2.197.1-28.2-g
Dimension 18
CM no
Base change no

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Base field \(\Q(\sqrt{197}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[28,14,-2w - 12]$
Label 2.2.197.1-28.2-g
Dimension 18
Is CM no
Is base change no
Parent newspace dimension 75

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{18} \) \(\mathstrut +\mathstrut 3x^{17} \) \(\mathstrut -\mathstrut 75x^{16} \) \(\mathstrut -\mathstrut 176x^{15} \) \(\mathstrut +\mathstrut 2320x^{14} \) \(\mathstrut +\mathstrut 3974x^{13} \) \(\mathstrut -\mathstrut 37693x^{12} \) \(\mathstrut -\mathstrut 44177x^{11} \) \(\mathstrut +\mathstrut 342933x^{10} \) \(\mathstrut +\mathstrut 264231x^{9} \) \(\mathstrut -\mathstrut 1762946x^{8} \) \(\mathstrut -\mathstrut 902541x^{7} \) \(\mathstrut +\mathstrut 5040389x^{6} \) \(\mathstrut +\mathstrut 1796166x^{5} \) \(\mathstrut -\mathstrut 7467415x^{4} \) \(\mathstrut -\mathstrut 2015434x^{3} \) \(\mathstrut +\mathstrut 4618804x^{2} \) \(\mathstrut +\mathstrut 1061984x \) \(\mathstrut -\mathstrut 379456\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}1$
7 $[7, 7, w - 7]$ $\phantom{-}e$
7 $[7, 7, w + 6]$ $-1$
9 $[9, 3, 3]$ $...$
19 $[19, 19, w + 5]$ $...$
19 $[19, 19, w - 6]$ $...$
23 $[23, 23, w + 8]$ $...$
23 $[23, 23, -w + 9]$ $...$
25 $[25, 5, 5]$ $...$
29 $[29, 29, -w - 4]$ $...$
29 $[29, 29, w - 5]$ $...$
37 $[37, 37, -w - 3]$ $...$
37 $[37, 37, w - 4]$ $...$
41 $[41, 41, -w - 9]$ $...$
41 $[41, 41, w - 10]$ $...$
43 $[43, 43, -w - 2]$ $...$
43 $[43, 43, w - 3]$ $...$
47 $[47, 47, -w - 1]$ $...$
47 $[47, 47, w - 2]$ $...$
53 $[53, 53, 2w - 13]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4,2,2]$ $-1$
7 $[7,7,-w - 6]$ $1$