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Properties

Label 63.8.o
Level $63$
Weight $8$
Character orbit 63.o
Rep. character $\chi_{63}(20,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $108$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 63.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(63, [\chi])\).

Total New Old
Modular forms 116 116 0
Cusp forms 108 108 0
Eisenstein series 8 8 0

Trace form

\( 108 q - 6 q^{2} + 3326 q^{4} + 82 q^{7} + 2652 q^{9} + 8856 q^{11} - 70320 q^{14} + 22326 q^{15} - 196354 q^{16} + 8166 q^{18} - 128544 q^{21} - 514 q^{22} + 137184 q^{23} - 718752 q^{25} + 75004 q^{28}+ \cdots - 79433088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.8.o.a 63.o 63.o $108$ $19.680$ None 63.8.o.a \(-6\) \(0\) \(0\) \(82\) $\mathrm{SU}(2)[C_{6}]$