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Properties

Label 33.8.f
Level $33$
Weight $8$
Character orbit 33.f
Rep. character $\chi_{33}(2,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $104$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 33.f (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(33, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

Trace form

\( 104 q - 42 q^{3} - 1542 q^{4} - 1725 q^{6} - 10 q^{7} + 550 q^{9} + 12942 q^{12} - 10 q^{13} - 21762 q^{15} - 40042 q^{16} + 60435 q^{18} + 10460 q^{19} - 218044 q^{22} + 330875 q^{24} + 462276 q^{25} - 294096 q^{27}+ \cdots + 46642084 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.8.f.a 33.f 33.f $104$ $10.309$ None 33.8.f.a \(0\) \(-42\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$