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Properties

Label 80.4.s
Level $80$
Weight $4$
Character orbit 80.s
Rep. character $\chi_{80}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 80.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(80, [\chi])\).

Total New Old
Modular forms 76 76 0
Cusp forms 68 68 0
Eisenstein series 8 8 0

Trace form

\( 68 q - 2 q^{2} - 4 q^{3} - 12 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} + 40 q^{8} + 540 q^{9} + 14 q^{10} - 4 q^{11} - 80 q^{12} - 108 q^{15} - 136 q^{16} - 4 q^{17} + 166 q^{18} + 24 q^{19} - 176 q^{20} - 4 q^{21}+ \cdots - 2764 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.4.s.a 80.s 80.s $68$ $4.720$ None 80.4.j.a \(-2\) \(-4\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$