Properties

Label 8.6.a
Level 8
Weight 6
Character orbit a
Rep. character \(\chi_{8}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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 irreducible Hecke orbits

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

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