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Properties

Label 16.4.a
Level $16$
Weight $4$
Character orbit 16.a
Rep. character $\chi_{16}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(16))\).

Total New Old
Modular forms 9 2 7
Cusp forms 3 1 2
Eisenstein series 6 1 5

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

\( q + 4 q^{3} - 2 q^{5} - 24 q^{7} - 11 q^{9} + 44 q^{11} + 22 q^{13} - 8 q^{15} + 50 q^{17} - 44 q^{19} - 96 q^{21} + 56 q^{23} - 121 q^{25} - 152 q^{27} + 198 q^{29} + 160 q^{31} + 176 q^{33} + 48 q^{35}+ \cdots - 484 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.4.a.a 16.a 1.a $1$ $0.944$ \(\Q\) None 8.4.a.a \(0\) \(4\) \(-2\) \(-24\) $+$ $\mathrm{SU}(2)$ \(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(16)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)