↑

Properties

Label 164.2.i
Level $164$
Weight $2$
Character orbit 164.i
Rep. character $\chi_{164}(3,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $76$
Newform subspaces $2$
Sturm bound $42$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.i (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(164, [\chi])\).

Total New Old
Modular forms 92 92 0
Cusp forms 76 76 0
Eisenstein series 16 16 0

Trace form

\( 76 q - 4 q^{2} - 8 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{10} - 12 q^{12} - 8 q^{13} - 16 q^{14} - 8 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{20} - 8 q^{21} + 20 q^{22} - 28 q^{24} - 4 q^{26} - 20 q^{28} - 12 q^{29}+ \cdots - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(164, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
164.2.i.a 164.i 164.i $4$ $1.310$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) 164.2.i.a \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{8}]$ \(q+(1+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{4}+4\zeta_{8}^{3}q^{5}+\cdots\)
164.2.i.b 164.i 164.i $72$ $1.310$ None 164.2.i.b \(-8\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$