Properties

Label 16.3.c
Level 16
Weight 3
Character orbit c
Rep. character \(\chi_{16}(15,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 16.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(16, [\chi])\).

Total New Old
Modular forms 7 1 6
Cusp forms 1 1 0
Eisenstein series 6 0 6

Trace form

\(q \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut +\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 70q^{37} \) \(\mathstrut +\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 54q^{45} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut +\mathstrut 90q^{53} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 60q^{65} \) \(\mathstrut -\mathstrut 110q^{73} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut +\mathstrut 180q^{85} \) \(\mathstrut -\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 130q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(16, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
16.3.c.a \(1\) \(0.436\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots\)