Properties

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

Related objects

Downloads

Learn more about

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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

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