Properties

Label 16.6.a
Level 16
Weight 6
Character orbit a
Rep. character \(\chi_{16}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 12
Trace bound 3

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 16.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(16))\).

Total New Old
Modular forms 13 3 10
Cusp forms 7 2 5
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.
\(+\)\(1\)
\(-\)\(1\)

Trace form

\(2q \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 112q^{7} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 112q^{7} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 664q^{11} \) \(\mathstrut +\mathstrut 60q^{13} \) \(\mathstrut +\mathstrut 2128q^{15} \) \(\mathstrut -\mathstrut 604q^{17} \) \(\mathstrut -\mathstrut 3880q^{19} \) \(\mathstrut +\mathstrut 576q^{21} \) \(\mathstrut +\mathstrut 3920q^{23} \) \(\mathstrut +\mathstrut 2142q^{25} \) \(\mathstrut -\mathstrut 2384q^{27} \) \(\mathstrut -\mathstrut 3876q^{29} \) \(\mathstrut +\mathstrut 1472q^{31} \) \(\mathstrut -\mathstrut 4000q^{33} \) \(\mathstrut +\mathstrut 2976q^{35} \) \(\mathstrut +\mathstrut 10028q^{37} \) \(\mathstrut -\mathstrut 14576q^{39} \) \(\mathstrut +\mathstrut 8340q^{41} \) \(\mathstrut +\mathstrut 21288q^{43} \) \(\mathstrut -\mathstrut 16964q^{45} \) \(\mathstrut -\mathstrut 22368q^{47} \) \(\mathstrut -\mathstrut 25294q^{49} \) \(\mathstrut +\mathstrut 31088q^{51} \) \(\mathstrut +\mathstrut 31180q^{53} \) \(\mathstrut -\mathstrut 19984q^{55} \) \(\mathstrut +\mathstrut 50848q^{57} \) \(\mathstrut -\mathstrut 9208q^{59} \) \(\mathstrut -\mathstrut 53220q^{61} \) \(\mathstrut -\mathstrut 4944q^{63} \) \(\mathstrut -\mathstrut 57944q^{65} \) \(\mathstrut -\mathstrut 6280q^{67} \) \(\mathstrut +\mathstrut 52928q^{69} \) \(\mathstrut +\mathstrut 78832q^{71} \) \(\mathstrut +\mathstrut 62676q^{73} \) \(\mathstrut -\mathstrut 49528q^{75} \) \(\mathstrut -\mathstrut 50496q^{77} \) \(\mathstrut +\mathstrut 32352q^{79} \) \(\mathstrut -\mathstrut 97742q^{81} \) \(\mathstrut -\mathstrut 135080q^{83} \) \(\mathstrut +\mathstrut 120728q^{85} \) \(\mathstrut +\mathstrut 58512q^{87} \) \(\mathstrut +\mathstrut 101748q^{89} \) \(\mathstrut -\mathstrut 25312q^{91} \) \(\mathstrut -\mathstrut 165632q^{93} \) \(\mathstrut +\mathstrut 180112q^{95} \) \(\mathstrut -\mathstrut 73532q^{97} \) \(\mathstrut +\mathstrut 33992q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(16))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
16.6.a.a \(1\) \(2.566\) \(\Q\) None \(0\) \(-20\) \(-74\) \(24\) \(+\) \(q-20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots\)
16.6.a.b \(1\) \(2.566\) \(\Q\) None \(0\) \(12\) \(54\) \(88\) \(-\) \(q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)