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Properties

Label 56.10.m
Level $56$
Weight $10$
Character orbit 56.m
Rep. character $\chi_{56}(3,\cdot)$
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.m (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

\( 140 q - 18 q^{2} - 6 q^{3} + 84 q^{4} + 17268 q^{8} + 433024 q^{9} - 26724 q^{10} - 65862 q^{11} - 82998 q^{12} - 214260 q^{14} + 410128 q^{16} - 6 q^{17} + 1110146 q^{18} - 6 q^{19} + 3455012 q^{22} - 5971242 q^{24}+ \cdots - 2771471384 q^{99}+O(q^{100}) \) 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.m.a 56.m 56.m $140$ $28.842$ None 56.10.m.a \(-18\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$