↑

Properties

Label 208.4.bj
Level $208$
Weight $4$
Character orbit 208.bj
Rep. character $\chi_{208}(29,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $328$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 208.bj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(208, [\chi])\).

Total New Old
Modular forms 344 344 0
Cusp forms 328 328 0
Eisenstein series 16 16 0

Trace form

\( 328 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 8 q^{5} - 32 q^{6} - 8 q^{8} - 2 q^{10} - 2 q^{11} - 116 q^{12} - 4 q^{13} - 248 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 40 q^{18} - 2 q^{19} - 42 q^{20} - 116 q^{21}+ \cdots + 7808 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(208, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
208.4.bj.a 208.bj 208.aj $328$ $12.272$ None 208.4.bj.a \(-2\) \(-2\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$