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Properties

Label 56.10.p
Level $56$
Weight $10$
Character orbit 56.p
Rep. character $\chi_{56}(37,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $140$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 56.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(56, [\chi])\).

Total New Old
Modular forms 148 148 0
Cusp forms 140 140 0
Eisenstein series 8 8 0

Trace form

\( 140 q + 16 q^{2} + 84 q^{4} - 1028 q^{6} - 4 q^{7} - 17276 q^{8} + 433024 q^{9} + 7882 q^{10} - 11702 q^{12} - 81490 q^{14} - 78740 q^{15} - 127080 q^{16} - 2 q^{17} - 1068734 q^{18} - 340000 q^{20} + 1664792 q^{22}+ \cdots + 3734018698 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(56, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
56.10.p.a 56.p 56.p $140$ $28.842$ None 56.10.p.a \(16\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$