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Properties

Label 80.10.q
Level $80$
Weight $10$
Character orbit 80.q
Rep. character $\chi_{80}(29,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $212$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 80.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(80, [\chi])\).

Total New Old
Modular forms 220 220 0
Cusp forms 212 212 0
Eisenstein series 8 8 0

Trace form

\( 212 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 17812 q^{10} - 4 q^{11} + 108500 q^{14} - 4 q^{15} - 534208 q^{16} + 480884 q^{19} + 2372984 q^{20} - 78736 q^{21} - 4888112 q^{24} - 7927240 q^{26} - 4 q^{29} - 34132064 q^{30}+ \cdots + 771348172 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.10.q.a 80.q 80.q $212$ $41.203$ None 80.10.q.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$