Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 7
Level $[7,7,2w + 19]$
Label 2.2.393.1-7.2-b
Dimension 74
CM no
Base change no

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Base field \(\Q(\sqrt{393}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 98\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[7,7,2w + 19]$
Label 2.2.393.1-7.2-b
Dimension 74
Is CM no
Is base change no
Parent newspace dimension 128

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{74} \) \(\mathstrut -\mathstrut 120x^{72} \) \(\mathstrut +\mathstrut 6886x^{70} \) \(\mathstrut -\mathstrut 251582x^{68} \) \(\mathstrut +\mathstrut 6573846x^{66} \) \(\mathstrut -\mathstrut 130835443x^{64} \) \(\mathstrut +\mathstrut 2062500975x^{62} \) \(\mathstrut -\mathstrut 26441321467x^{60} \) \(\mathstrut +\mathstrut 280879967299x^{58} \) \(\mathstrut -\mathstrut 2506489696838x^{56} \) \(\mathstrut +\mathstrut 18983394607391x^{54} \) \(\mathstrut -\mathstrut 122971461542199x^{52} \) \(\mathstrut +\mathstrut 685305354201788x^{50} \) \(\mathstrut -\mathstrut 3299758885574328x^{48} \) \(\mathstrut +\mathstrut 13769843720361027x^{46} \) \(\mathstrut -\mathstrut 49899772360606229x^{44} \) \(\mathstrut +\mathstrut 157204330573013486x^{42} \) \(\mathstrut -\mathstrut 430662208504018427x^{40} \) \(\mathstrut +\mathstrut 1025375594229965011x^{38} \) \(\mathstrut -\mathstrut 2119029229240490342x^{36} \) \(\mathstrut +\mathstrut 3793106964609972201x^{34} \) \(\mathstrut -\mathstrut 5864091279244172519x^{32} \) \(\mathstrut +\mathstrut 7800365890053553784x^{30} \) \(\mathstrut -\mathstrut 8885295241695589278x^{28} \) \(\mathstrut +\mathstrut 8616154674635115847x^{26} \) \(\mathstrut -\mathstrut 7061534501336086469x^{24} \) \(\mathstrut +\mathstrut 4848174519457649477x^{22} \) \(\mathstrut -\mathstrut 2758118369526408277x^{20} \) \(\mathstrut +\mathstrut 1282693816243401975x^{18} \) \(\mathstrut -\mathstrut 479416013373834168x^{16} \) \(\mathstrut +\mathstrut 140895342891278328x^{14} \) \(\mathstrut -\mathstrut 31635359529778060x^{12} \) \(\mathstrut +\mathstrut 5216674766413213x^{10} \) \(\mathstrut -\mathstrut 596483185109956x^{8} \) \(\mathstrut +\mathstrut 43136399919953x^{6} \) \(\mathstrut -\mathstrut 1659648409446x^{4} \) \(\mathstrut +\mathstrut 21795779240x^{2} \) \(\mathstrut -\mathstrut 19727140\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $...$
2 $[2, 2, -17w + 177]$ $\phantom{-}e$
3 $[3, 3, -842w + 8767]$ $...$
7 $[7, 7, -2w + 21]$ $...$
7 $[7, 7, 2w + 19]$ $-1$
13 $[13, 13, -12w - 113]$ $...$
13 $[13, 13, 12w - 125]$ $...$
17 $[17, 17, 182w - 1895]$ $...$
17 $[17, 17, 182w + 1713]$ $...$
23 $[23, 23, -512w - 4819]$ $...$
23 $[23, 23, 512w - 5331]$ $...$
25 $[25, 5, -5]$ $...$
29 $[29, 29, 22w - 229]$ $...$
29 $[29, 29, 22w + 207]$ $...$
43 $[43, 43, 114w + 1073]$ $...$
43 $[43, 43, 114w - 1187]$ $...$
47 $[47, 47, 8w - 83]$ $...$
47 $[47, 47, -8w - 75]$ $...$
61 $[61, 61, -1172w - 11031]$ $...$
61 $[61, 61, 1172w - 12203]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7,7,2w + 19]$ $1$