Properties

Label 16.5.c
Level 16
Weight 5
Character orbit c
Rep. character \(\chi_{16}(15,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 16.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(16, [\chi])\).

Total New Old
Modular forms 11 2 9
Cusp forms 5 2 3
Eisenstein series 6 0 6

Trace form

\(2q \) \(\mathstrut +\mathstrut 36q^{5} \) \(\mathstrut -\mathstrut 222q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 36q^{5} \) \(\mathstrut -\mathstrut 222q^{9} \) \(\mathstrut +\mathstrut 356q^{13} \) \(\mathstrut -\mathstrut 252q^{17} \) \(\mathstrut +\mathstrut 768q^{21} \) \(\mathstrut -\mathstrut 602q^{25} \) \(\mathstrut -\mathstrut 2844q^{29} \) \(\mathstrut +\mathstrut 3456q^{33} \) \(\mathstrut +\mathstrut 1060q^{37} \) \(\mathstrut +\mathstrut 324q^{41} \) \(\mathstrut -\mathstrut 3996q^{45} \) \(\mathstrut +\mathstrut 3266q^{49} \) \(\mathstrut +\mathstrut 1188q^{53} \) \(\mathstrut -\mathstrut 11136q^{57} \) \(\mathstrut +\mathstrut 1252q^{61} \) \(\mathstrut +\mathstrut 6408q^{65} \) \(\mathstrut +\mathstrut 20736q^{69} \) \(\mathstrut -\mathstrut 13372q^{73} \) \(\mathstrut -\mathstrut 6912q^{77} \) \(\mathstrut -\mathstrut 6462q^{81} \) \(\mathstrut -\mathstrut 4536q^{85} \) \(\mathstrut +\mathstrut 16452q^{89} \) \(\mathstrut -\mathstrut 9216q^{93} \) \(\mathstrut -\mathstrut 3196q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(16, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
16.5.c.a \(2\) \(1.654\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(36\) \(0\) \(q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)