Properties

Label 8.8.a
Level $8$
Weight $8$
Character orbit 8.a
Rep. character $\chi_{8}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $8$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 9 2 7
Cusp forms 5 2 3
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.
\(+\)\(1\)
\(-\)\(1\)

Trace form

\( 2 q - 40 q^{3} + 348 q^{5} - 1680 q^{7} + 4618 q^{9} + O(q^{10}) \) \( 2 q - 40 q^{3} + 348 q^{5} - 1680 q^{7} + 4618 q^{9} - 5688 q^{11} - 4660 q^{13} + 25808 q^{15} - 27420 q^{17} - 1352 q^{19} - 15552 q^{21} + 83280 q^{23} + 35374 q^{25} - 332560 q^{27} + 222636 q^{29} + 210880 q^{31} + 72800 q^{33} - 488928 q^{35} - 471780 q^{37} + 1174544 q^{39} - 177996 q^{41} + 20360 q^{43} - 507188 q^{45} - 397920 q^{47} + 59026 q^{49} + 220720 q^{51} + 2109180 q^{53} - 1153552 q^{55} - 587360 q^{57} - 1863576 q^{59} + 1002860 q^{61} - 1913040 q^{63} + 3514536 q^{65} + 7625560 q^{67} - 6793792 q^{69} - 5259024 q^{71} - 7351180 q^{73} + 10695784 q^{75} + 5023680 q^{77} - 1086112 q^{79} + 4104658 q^{81} - 6949320 q^{83} - 6081800 q^{85} - 2978160 q^{87} + 5132628 q^{89} - 2573664 q^{91} + 14460160 q^{93} - 2692848 q^{95} + 4865860 q^{97} - 11495192 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
8.8.a.a 8.a 1.a $1$ $2.499$ \(\Q\) None \(0\) \(-84\) \(-82\) \(-456\) $-$ $\mathrm{SU}(2)$ \(q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots\)
8.8.a.b 8.a 1.a $1$ $2.499$ \(\Q\) None \(0\) \(44\) \(430\) \(-1224\) $+$ $\mathrm{SU}(2)$ \(q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots\)

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

\( S_{8}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)