Properties

Label 4.6.a
Level $4$
Weight $6$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

\( q - 12 q^{3} + 54 q^{5} - 88 q^{7} - 99 q^{9} + 540 q^{11} - 418 q^{13} - 648 q^{15} + 594 q^{17} + 836 q^{19} + 1056 q^{21} - 4104 q^{23} - 209 q^{25} + 4104 q^{27} - 594 q^{29} + 4256 q^{31} - 6480 q^{33}+ \cdots - 53460 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
4.6.a.a 4.a 1.a $1$ $0.642$ \(\Q\) None 4.6.a.a \(0\) \(-12\) \(54\) \(-88\) $-$ $\mathrm{SU}(2)$ \(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)