↑

Properties

Label 65.4.n
Level $65$
Weight $4$
Character orbit 65.n
Rep. character $\chi_{65}(9,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 65.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(65, [\chi])\).

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

\( 36 q + 54 q^{4} + 10 q^{5} - 34 q^{6} + 72 q^{9} - 57 q^{10} + 4 q^{11} + 280 q^{14} + 102 q^{15} - 126 q^{16} + 8 q^{19} - 191 q^{20} - 100 q^{21} + 140 q^{24} - 282 q^{25} - 420 q^{26} - 540 q^{29} - 96 q^{30}+ \cdots - 5204 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(65, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
65.4.n.a 65.n 65.n $36$ $3.835$ None 65.4.n.a \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{6}]$