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Properties

Label 80.5.r
Level $80$
Weight $5$
Character orbit 80.r
Rep. character $\chi_{80}(11,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 80.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(80, [\chi])\).

Total New Old
Modular forms 100 64 36
Cusp forms 92 64 28
Eisenstein series 8 0 8

Trace form

\( 64 q + 12 q^{4} - 132 q^{6} - 100 q^{10} - 192 q^{11} - 60 q^{12} - 372 q^{14} - 144 q^{16} - 2720 q^{18} + 704 q^{19} - 600 q^{20} - 2364 q^{22} - 2304 q^{23} + 1800 q^{24} + 2064 q^{26} + 3648 q^{27}+ \cdots - 49216 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.5.r.a 80.r 16.f $64$ $8.270$ None 80.5.r.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)