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

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

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

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