Properties

Label 2.8.a
Level $2$
Weight $8$
Character orbit 2.a
Rep. character $\chi_{2}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(2))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim
\(+\)\(1\)

Trace form

\( q - 8 q^{2} + 12 q^{3} + 64 q^{4} - 210 q^{5} - 96 q^{6} + 1016 q^{7} - 512 q^{8} - 2043 q^{9} + 1680 q^{10} + 1092 q^{11} + 768 q^{12} + 1382 q^{13} - 8128 q^{14} - 2520 q^{15} + 4096 q^{16} + 14706 q^{17}+ \cdots - 2230956 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
2.8.a.a 2.a 1.a $1$ $0.625$ \(\Q\) None 2.8.a.a \(-8\) \(12\) \(-210\) \(1016\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots\)