Properties

Label 8.22.a
Level $8$
Weight $22$
Character orbit 8.a
Rep. character $\chi_{8}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $22$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 8.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(22\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(8))\).

Total New Old
Modular forms 23 5 18
Cusp forms 19 5 14
Eisenstein series 4 0 4

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
\(+\)\(2\)
\(-\)\(3\)

Trace form

\( 5 q - 8668 q^{3} - 22003634 q^{5} + 740760072 q^{7} + 29917044817 q^{9} + 13471294636 q^{11} - 356632250986 q^{13} - 1862971179880 q^{15} + 1203867602330 q^{17} + 55090597707316 q^{19} + 63483640028832 q^{21}+ \cdots + 81\!\cdots\!44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(8))\) 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
8.22.a.a 8.a 1.a $2$ $22.358$ \(\Q(\sqrt{358549}) \) None 8.22.a.a \(0\) \(-105432\) \(2108140\) \(444771792\) $+$ $\mathrm{SU}(2)$ \(q+(-52716-\beta )q^{3}+(1054070+20\beta )q^{5}+\cdots\)
8.22.a.b 8.a 1.a $3$ $22.358$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 8.22.a.b \(0\) \(96764\) \(-24111774\) \(295988280\) $-$ $\mathrm{SU}(2)$ \(q+(32255-\beta _{1})q^{3}+(-8037261+9\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(8)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)