Properties

Label 16.8.a
Level 16
Weight 8
Character orbit a
Rep. character \(\chi_{16}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 16
Trace bound 3

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 16.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(16))\).

Total New Old
Modular forms 17 4 13
Cusp forms 11 3 8
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.
\(+\)\(2\)
\(-\)\(1\)

Trace form

\(3q \) \(\mathstrut +\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 138q^{5} \) \(\mathstrut +\mathstrut 664q^{7} \) \(\mathstrut +\mathstrut 2575q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 138q^{5} \) \(\mathstrut +\mathstrut 664q^{7} \) \(\mathstrut +\mathstrut 2575q^{9} \) \(\mathstrut +\mathstrut 4596q^{11} \) \(\mathstrut -\mathstrut 3278q^{13} \) \(\mathstrut -\mathstrut 23288q^{15} \) \(\mathstrut -\mathstrut 12714q^{17} \) \(\mathstrut +\mathstrut 41292q^{19} \) \(\mathstrut -\mathstrut 3360q^{21} \) \(\mathstrut -\mathstrut 151992q^{23} \) \(\mathstrut +\mathstrut 1349q^{25} \) \(\mathstrut +\mathstrut 383320q^{27} \) \(\mathstrut +\mathstrut 120066q^{29} \) \(\mathstrut -\mathstrut 438432q^{31} \) \(\mathstrut +\mathstrut 85904q^{33} \) \(\mathstrut +\mathstrut 702288q^{35} \) \(\mathstrut -\mathstrut 311254q^{37} \) \(\mathstrut -\mathstrut 1191128q^{39} \) \(\mathstrut -\mathstrut 167154q^{41} \) \(\mathstrut +\mathstrut 610388q^{43} \) \(\mathstrut -\mathstrut 78158q^{45} \) \(\mathstrut -\mathstrut 74736q^{47} \) \(\mathstrut +\mathstrut 267739q^{49} \) \(\mathstrut -\mathstrut 397192q^{51} \) \(\mathstrut +\mathstrut 615162q^{53} \) \(\mathstrut +\mathstrut 1382872q^{55} \) \(\mathstrut -\mathstrut 1066640q^{57} \) \(\mathstrut -\mathstrut 777084q^{59} \) \(\mathstrut +\mathstrut 1830562q^{61} \) \(\mathstrut +\mathstrut 3988728q^{63} \) \(\mathstrut +\mathstrut 3224316q^{65} \) \(\mathstrut -\mathstrut 7499556q^{67} \) \(\mathstrut -\mathstrut 5969248q^{69} \) \(\mathstrut +\mathstrut 6673752q^{71} \) \(\mathstrut -\mathstrut 6370898q^{73} \) \(\mathstrut -\mathstrut 10287484q^{75} \) \(\mathstrut +\mathstrut 6133152q^{77} \) \(\mathstrut +\mathstrut 4652912q^{79} \) \(\mathstrut +\mathstrut 7963579q^{81} \) \(\mathstrut +\mathstrut 1276428q^{83} \) \(\mathstrut -\mathstrut 9170060q^{85} \) \(\mathstrut +\mathstrut 4209000q^{87} \) \(\mathstrut -\mathstrut 6818562q^{89} \) \(\mathstrut +\mathstrut 1169552q^{91} \) \(\mathstrut +\mathstrut 17190784q^{93} \) \(\mathstrut -\mathstrut 5694552q^{95} \) \(\mathstrut +\mathstrut 13548006q^{97} \) \(\mathstrut +\mathstrut 13726148q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(16))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
16.8.a.a \(1\) \(4.998\) \(\Q\) None \(0\) \(-44\) \(430\) \(1224\) \(+\) \(q-44q^{3}+430q^{5}+1224q^{7}-251q^{9}+\cdots\)
16.8.a.b \(1\) \(4.998\) \(\Q\) None \(0\) \(-12\) \(-210\) \(-1016\) \(-\) \(q-12q^{3}-210q^{5}-1016q^{7}-2043q^{9}+\cdots\)
16.8.a.c \(1\) \(4.998\) \(\Q\) None \(0\) \(84\) \(-82\) \(456\) \(+\) \(q+84q^{3}-82q^{5}+456q^{7}+4869q^{9}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

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