Properties

Label 8.6.a
Level 8
Weight 6
Character orbit a
Rep. character \(\chi_{8}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 8.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(8))\).

Total New Old
Modular forms 7 1 6
Cusp forms 3 1 2
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim.
\(-\)\(1\)

Trace form

\( q + 20q^{3} - 74q^{5} - 24q^{7} + 157q^{9} + O(q^{10}) \) \( q + 20q^{3} - 74q^{5} - 24q^{7} + 157q^{9} + 124q^{11} + 478q^{13} - 1480q^{15} - 1198q^{17} + 3044q^{19} - 480q^{21} + 184q^{23} + 2351q^{25} - 1720q^{27} - 3282q^{29} - 5728q^{31} + 2480q^{33} + 1776q^{35} + 10326q^{37} + 9560q^{39} - 8886q^{41} - 9188q^{43} - 11618q^{45} + 23664q^{47} - 16231q^{49} - 23960q^{51} + 11686q^{53} - 9176q^{55} + 60880q^{57} + 16876q^{59} - 18482q^{61} - 3768q^{63} - 35372q^{65} - 15532q^{67} + 3680q^{69} - 31960q^{71} - 4886q^{73} + 47020q^{75} - 2976q^{77} + 44560q^{79} - 72551q^{81} + 67364q^{83} + 88652q^{85} - 65640q^{87} + 71994q^{89} - 11472q^{91} - 114560q^{93} - 225256q^{95} + 48866q^{97} + 19468q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(8))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
8.6.a.a \(1\) \(1.283\) \(\Q\) None \(0\) \(20\) \(-74\) \(-24\) \(-\) \(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 20 T + 243 T^{2} \)
$5$ \( 1 + 74 T + 3125 T^{2} \)
$7$ \( 1 + 24 T + 16807 T^{2} \)
$11$ \( 1 - 124 T + 161051 T^{2} \)
$13$ \( 1 - 478 T + 371293 T^{2} \)
$17$ \( 1 + 1198 T + 1419857 T^{2} \)
$19$ \( 1 - 3044 T + 2476099 T^{2} \)
$23$ \( 1 - 184 T + 6436343 T^{2} \)
$29$ \( 1 + 3282 T + 20511149 T^{2} \)
$31$ \( 1 + 5728 T + 28629151 T^{2} \)
$37$ \( 1 - 10326 T + 69343957 T^{2} \)
$41$ \( 1 + 8886 T + 115856201 T^{2} \)
$43$ \( 1 + 9188 T + 147008443 T^{2} \)
$47$ \( 1 - 23664 T + 229345007 T^{2} \)
$53$ \( 1 - 11686 T + 418195493 T^{2} \)
$59$ \( 1 - 16876 T + 714924299 T^{2} \)
$61$ \( 1 + 18482 T + 844596301 T^{2} \)
$67$ \( 1 + 15532 T + 1350125107 T^{2} \)
$71$ \( 1 + 31960 T + 1804229351 T^{2} \)
$73$ \( 1 + 4886 T + 2073071593 T^{2} \)
$79$ \( 1 - 44560 T + 3077056399 T^{2} \)
$83$ \( 1 - 67364 T + 3939040643 T^{2} \)
$89$ \( 1 - 71994 T + 5584059449 T^{2} \)
$97$ \( 1 - 48866 T + 8587340257 T^{2} \)
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