Properties

Label 16.10.a
Level 16
Weight 10
Character orbit a
Rep. character \(\chi_{16}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 4
Sturm bound 20
Trace bound 3

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 16.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(20\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(16))\).

Total New Old
Modular forms 21 5 16
Cusp forms 15 4 11
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.
\(+\)\(2\)
\(-\)\(2\)

Trace form

\(4q \) \(\mathstrut -\mathstrut 80q^{3} \) \(\mathstrut -\mathstrut 360q^{5} \) \(\mathstrut +\mathstrut 1376q^{7} \) \(\mathstrut +\mathstrut 5812q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 80q^{3} \) \(\mathstrut -\mathstrut 360q^{5} \) \(\mathstrut +\mathstrut 1376q^{7} \) \(\mathstrut +\mathstrut 5812q^{9} \) \(\mathstrut -\mathstrut 10992q^{11} \) \(\mathstrut -\mathstrut 43080q^{13} \) \(\mathstrut +\mathstrut 60448q^{15} \) \(\mathstrut +\mathstrut 172104q^{17} \) \(\mathstrut -\mathstrut 296336q^{19} \) \(\mathstrut -\mathstrut 336768q^{21} \) \(\mathstrut +\mathstrut 1349664q^{23} \) \(\mathstrut -\mathstrut 30468q^{25} \) \(\mathstrut -\mathstrut 5005088q^{27} \) \(\mathstrut +\mathstrut 1723896q^{29} \) \(\mathstrut +\mathstrut 13751680q^{31} \) \(\mathstrut -\mathstrut 3529024q^{33} \) \(\mathstrut -\mathstrut 27870144q^{35} \) \(\mathstrut +\mathstrut 1408792q^{37} \) \(\mathstrut +\mathstrut 46429600q^{39} \) \(\mathstrut +\mathstrut 4797864q^{41} \) \(\mathstrut -\mathstrut 78798192q^{43} \) \(\mathstrut -\mathstrut 6847304q^{45} \) \(\mathstrut +\mathstrut 139372608q^{47} \) \(\mathstrut +\mathstrut 3427300q^{49} \) \(\mathstrut -\mathstrut 202646944q^{51} \) \(\mathstrut -\mathstrut 10028712q^{53} \) \(\mathstrut +\mathstrut 216893536q^{55} \) \(\mathstrut +\mathstrut 25903936q^{57} \) \(\mathstrut -\mathstrut 224197296q^{59} \) \(\mathstrut -\mathstrut 10080648q^{61} \) \(\mathstrut +\mathstrut 293290464q^{63} \) \(\mathstrut -\mathstrut 64788144q^{65} \) \(\mathstrut -\mathstrut 255761744q^{67} \) \(\mathstrut +\mathstrut 121435520q^{69} \) \(\mathstrut -\mathstrut 39174048q^{71} \) \(\mathstrut -\mathstrut 15735768q^{73} \) \(\mathstrut +\mathstrut 276237392q^{75} \) \(\mathstrut -\mathstrut 120707712q^{77} \) \(\mathstrut -\mathstrut 341312064q^{79} \) \(\mathstrut -\mathstrut 113638172q^{81} \) \(\mathstrut +\mathstrut 758656368q^{83} \) \(\mathstrut +\mathstrut 277817008q^{85} \) \(\mathstrut -\mathstrut 1417283424q^{87} \) \(\mathstrut +\mathstrut 573376104q^{89} \) \(\mathstrut +\mathstrut 1721466688q^{91} \) \(\mathstrut -\mathstrut 1004178944q^{93} \) \(\mathstrut -\mathstrut 2153970528q^{95} \) \(\mathstrut -\mathstrut 728181880q^{97} \) \(\mathstrut +\mathstrut 2808900560q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(16))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
16.10.a.a \(1\) \(8.241\) \(\Q\) None \(0\) \(-228\) \(-666\) \(6328\) \(-\) \(q-228q^{3}-666q^{5}+6328q^{7}+32301q^{9}+\cdots\)
16.10.a.b \(1\) \(8.241\) \(\Q\) None \(0\) \(-68\) \(1510\) \(-10248\) \(+\) \(q-68q^{3}+1510q^{5}-10248q^{7}-15059q^{9}+\cdots\)
16.10.a.c \(1\) \(8.241\) \(\Q\) None \(0\) \(60\) \(-2074\) \(4344\) \(+\) \(q+60q^{3}-2074q^{5}+4344q^{7}-16083q^{9}+\cdots\)
16.10.a.d \(1\) \(8.241\) \(\Q\) None \(0\) \(156\) \(870\) \(952\) \(-\) \(q+156q^{3}+870q^{5}+952q^{7}+4653q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)