Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 7
Level $[7, 7, 6w - 35]$
Label 2.2.113.1-7.1-c
Dimension 10
CM no
Base change no

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Base field \(\Q(\sqrt{113}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[7, 7, 6w - 35]$
Label 2.2.113.1-7.1-c
Dimension 10
Is CM no
Is base change no
Parent newspace dimension 17

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} \) \(\mathstrut -\mathstrut 3x^{9} \) \(\mathstrut -\mathstrut 12x^{8} \) \(\mathstrut +\mathstrut 40x^{7} \) \(\mathstrut +\mathstrut 37x^{6} \) \(\mathstrut -\mathstrut 162x^{5} \) \(\mathstrut -\mathstrut 7x^{4} \) \(\mathstrut +\mathstrut 199x^{3} \) \(\mathstrut -\mathstrut 5x^{2} \) \(\mathstrut -\mathstrut 80x \) \(\mathstrut -\mathstrut 12\)

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Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $-\frac{1}{2}e^{8} + 6e^{6} - e^{5} - \frac{41}{2}e^{4} + \frac{15}{2}e^{3} + 18e^{2} - \frac{13}{2}e - 4$
7 $[7, 7, 6w - 35]$ $-1$
7 $[7, 7, -6w - 29]$ $-\frac{1}{2}e^{9} + e^{8} + 7e^{7} - 12e^{6} - \frac{61}{2}e^{5} + \frac{79}{2}e^{4} + 44e^{3} - \frac{47}{2}e^{2} - 27e - 4$
9 $[9, 3, 3]$ $\phantom{-}\frac{3}{2}e^{9} - \frac{1}{2}e^{8} - 19e^{7} + 8e^{6} + \frac{145}{2}e^{5} - 34e^{4} - \frac{173}{2}e^{3} + \frac{39}{2}e^{2} + \frac{77}{2}e + 4$
11 $[11, 11, 4w + 19]$ $-\frac{5}{2}e^{9} + e^{8} + 33e^{7} - 15e^{6} - \frac{271}{2}e^{5} + \frac{123}{2}e^{4} + 187e^{3} - \frac{77}{2}e^{2} - 89e - 12$
11 $[11, 11, 4w - 23]$ $\phantom{-}\frac{3}{2}e^{9} - e^{8} - 19e^{7} + 14e^{6} + \frac{143}{2}e^{5} - \frac{109}{2}e^{4} - 79e^{3} + \frac{75}{2}e^{2} + 32e - 1$
13 $[13, 13, -2w + 11]$ $\phantom{-}\frac{5}{2}e^{9} - 2e^{8} - 34e^{7} + 26e^{6} + \frac{289}{2}e^{5} - \frac{189}{2}e^{4} - 204e^{3} + \frac{127}{2}e^{2} + 94e + 8$
13 $[13, 13, 2w + 9]$ $-2e^{9} + 2e^{8} + 27e^{7} - 25e^{6} - 113e^{5} + 85e^{4} + 155e^{3} - 42e^{2} - 79e - 18$
25 $[25, 5, -5]$ $\phantom{-}e^{7} - 12e^{5} + e^{4} + 40e^{3} - 7e^{2} - 29e$
31 $[31, 31, 2w - 13]$ $-\frac{5}{2}e^{9} + \frac{3}{2}e^{8} + 32e^{7} - 21e^{6} - \frac{247}{2}e^{5} + 82e^{4} + \frac{293}{2}e^{3} - \frac{111}{2}e^{2} - \frac{119}{2}e - 2$
31 $[31, 31, -2w - 11]$ $-\frac{5}{2}e^{9} - e^{8} + 33e^{7} + 9e^{6} - \frac{279}{2}e^{5} - \frac{41}{2}e^{4} + 215e^{3} + \frac{65}{2}e^{2} - 103e - 25$
41 $[41, 41, -8w - 39]$ $\phantom{-}\frac{1}{2}e^{9} - 2e^{8} - 6e^{7} + 25e^{6} + \frac{35}{2}e^{5} - \frac{179}{2}e^{4} + 3e^{3} + \frac{151}{2}e^{2} - 2e - 10$
41 $[41, 41, 8w - 47]$ $\phantom{-}\frac{9}{2}e^{9} - \frac{5}{2}e^{8} - 61e^{7} + 33e^{6} + \frac{521}{2}e^{5} - 119e^{4} - \frac{759}{2}e^{3} + \frac{119}{2}e^{2} + \frac{361}{2}e + 32$
53 $[53, 53, -26w - 125]$ $\phantom{-}\frac{11}{2}e^{9} - 4e^{8} - 74e^{7} + 53e^{6} + \frac{623}{2}e^{5} - \frac{391}{2}e^{4} - 443e^{3} + \frac{247}{2}e^{2} + 225e + 30$
53 $[53, 53, 26w - 151]$ $\phantom{-}e^{9} - e^{8} - 13e^{7} + 14e^{6} + 52e^{5} - 57e^{4} - 69e^{3} + 54e^{2} + 37e - 4$
61 $[61, 61, -14w + 81]$ $-\frac{11}{2}e^{9} + 3e^{8} + 69e^{7} - 44e^{6} - \frac{513}{2}e^{5} + \frac{355}{2}e^{4} + 280e^{3} - \frac{229}{2}e^{2} - 112e - 17$
61 $[61, 61, -14w - 67]$ $-e^{9} + 14e^{7} - 65e^{5} - 4e^{4} + 116e^{3} + 30e^{2} - 70e - 26$
83 $[83, 83, 2w - 15]$ $\phantom{-}\frac{11}{2}e^{9} - 4e^{8} - 76e^{7} + 51e^{6} + \frac{667}{2}e^{5} - \frac{357}{2}e^{4} - 507e^{3} + \frac{191}{2}e^{2} + 261e + 41$
83 $[83, 83, -2w - 13]$ $-\frac{3}{2}e^{9} + \frac{1}{2}e^{8} + 23e^{7} - 5e^{6} - \frac{235}{2}e^{5} + 8e^{4} + \frac{447}{2}e^{3} + \frac{55}{2}e^{2} - \frac{257}{2}e - 32$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, 6w - 35]$ $1$