Properties

Label 4.6.a
Level 4
Weight 6
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 4.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(4))\).

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

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

\( q - 12q^{3} + 54q^{5} - 88q^{7} - 99q^{9} + O(q^{10}) \) \( q - 12q^{3} + 54q^{5} - 88q^{7} - 99q^{9} + 540q^{11} - 418q^{13} - 648q^{15} + 594q^{17} + 836q^{19} + 1056q^{21} - 4104q^{23} - 209q^{25} + 4104q^{27} - 594q^{29} + 4256q^{31} - 6480q^{33} - 4752q^{35} - 298q^{37} + 5016q^{39} + 17226q^{41} - 12100q^{43} - 5346q^{45} - 1296q^{47} - 9063q^{49} - 7128q^{51} + 19494q^{53} + 29160q^{55} - 10032q^{57} - 7668q^{59} - 34738q^{61} + 8712q^{63} - 22572q^{65} + 21812q^{67} + 49248q^{69} - 46872q^{71} + 67562q^{73} + 2508q^{75} - 47520q^{77} - 76912q^{79} - 25191q^{81} + 67716q^{83} + 32076q^{85} + 7128q^{87} + 29754q^{89} + 36784q^{91} - 51072q^{93} + 45144q^{95} - 122398q^{97} - 53460q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.6.a.a \(1\) \(0.642\) \(\Q\) None \(0\) \(-12\) \(54\) \(-88\) \(-\) \(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)