Properties

Label 16.4.a
Level 16
Weight 4
Character orbit a
Rep. character \(\chi_{16}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(16))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
16.4.a.a \(1\) \(0.944\) \(\Q\) None \(0\) \(4\) \(-2\) \(-24\) \(+\) \(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)

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

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