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

\( q + 4 q^{3} - 2 q^{5} - 24 q^{7} - 11 q^{9} + O(q^{10}) \) \( q + 4 q^{3} - 2 q^{5} - 24 q^{7} - 11 q^{9} + 44 q^{11} + 22 q^{13} - 8 q^{15} + 50 q^{17} - 44 q^{19} - 96 q^{21} + 56 q^{23} - 121 q^{25} - 152 q^{27} + 198 q^{29} + 160 q^{31} + 176 q^{33} + 48 q^{35} - 162 q^{37} + 88 q^{39} - 198 q^{41} - 52 q^{43} + 22 q^{45} - 528 q^{47} + 233 q^{49} + 200 q^{51} - 242 q^{53} - 88 q^{55} - 176 q^{57} + 668 q^{59} + 550 q^{61} + 264 q^{63} - 44 q^{65} - 188 q^{67} + 224 q^{69} - 728 q^{71} + 154 q^{73} - 484 q^{75} - 1056 q^{77} + 656 q^{79} - 311 q^{81} - 236 q^{83} - 100 q^{85} + 792 q^{87} + 714 q^{89} - 528 q^{91} + 640 q^{93} + 88 q^{95} - 478 q^{97} - 484 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label Char Prim Dim $A$ Field CM 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 \(0\) \(4\) \(-2\) \(-24\) $+$ $\mathrm{SU}(2)$ \(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)

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

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