Properties

Base field \(\Q(\sqrt{197}) \)
Weight [2, 2]
Level norm 23
Level $[23, 23, w + 8]$
Label 2.2.197.1-23.1-c
Dimension 34
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 $[23, 23, w + 8]$
Label 2.2.197.1-23.1-c
Dimension 34
Is CM no
Is base change no
Parent newspace dimension 81

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{34} \) \(\mathstrut +\mathstrut 6x^{33} \) \(\mathstrut -\mathstrut 64x^{32} \) \(\mathstrut -\mathstrut 424x^{31} \) \(\mathstrut +\mathstrut 1770x^{30} \) \(\mathstrut +\mathstrut 13292x^{29} \) \(\mathstrut -\mathstrut 27918x^{28} \) \(\mathstrut -\mathstrut 245359x^{27} \) \(\mathstrut +\mathstrut 279741x^{26} \) \(\mathstrut +\mathstrut 2984856x^{25} \) \(\mathstrut -\mathstrut 1887901x^{24} \) \(\mathstrut -\mathstrut 25363915x^{23} \) \(\mathstrut +\mathstrut 9020266x^{22} \) \(\mathstrut +\mathstrut 155522086x^{21} \) \(\mathstrut -\mathstrut 33007342x^{20} \) \(\mathstrut -\mathstrut 699955090x^{19} \) \(\mathstrut +\mathstrut 105465900x^{18} \) \(\mathstrut +\mathstrut 2325984857x^{17} \) \(\mathstrut -\mathstrut 323151722x^{16} \) \(\mathstrut -\mathstrut 5685880095x^{15} \) \(\mathstrut +\mathstrut 878189527x^{14} \) \(\mathstrut +\mathstrut 10090669043x^{13} \) \(\mathstrut -\mathstrut 1813609905x^{12} \) \(\mathstrut -\mathstrut 12693014291x^{11} \) \(\mathstrut +\mathstrut 2537362006x^{10} \) \(\mathstrut +\mathstrut 10894619315x^{9} \) \(\mathstrut -\mathstrut 2185785281x^{8} \) \(\mathstrut -\mathstrut 6016229092x^{7} \) \(\mathstrut +\mathstrut 998123180x^{6} \) \(\mathstrut +\mathstrut 1946184690x^{5} \) \(\mathstrut -\mathstrut 153475734x^{4} \) \(\mathstrut -\mathstrut 310007709x^{3} \) \(\mathstrut -\mathstrut 16784172x^{2} \) \(\mathstrut +\mathstrut 12803090x \) \(\mathstrut +\mathstrut 1214263\)

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Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
7 $[7, 7, w - 7]$ $...$
7 $[7, 7, w + 6]$ $...$
9 $[9, 3, 3]$ $...$
19 $[19, 19, w + 5]$ $...$
19 $[19, 19, w - 6]$ $...$
23 $[23, 23, w + 8]$ $\phantom{-}1$
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
23 $[23, 23, w + 8]$ $-1$