↑

Properties

Label 16.4.e
Level $16$
Weight $4$
Character orbit 16.e
Rep. character $\chi_{16}(5,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(16, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 32 q^{6} - 44 q^{8} - 68 q^{10} + 18 q^{11} + 100 q^{12} - 2 q^{13} + 188 q^{14} - 124 q^{15} + 280 q^{16} - 4 q^{17} + 174 q^{18} - 26 q^{19} - 196 q^{20}+ \cdots + 4958 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.4.e.a 16.e 16.e $10$ $0.944$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 16.4.e.a \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)