Properties

Label 28.5.g
Level $28$
Weight $5$
Character orbit 28.g
Rep. character $\chi_{28}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 28.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(28, [\chi])\).

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

Trace form

\( 28 q + 2 q^{2} - 4 q^{4} - 2 q^{5} - 36 q^{6} - 184 q^{8} + 268 q^{9} + 130 q^{10} - 48 q^{12} + 344 q^{13} - 474 q^{14} - 432 q^{16} - 2 q^{17} - 568 q^{18} + 664 q^{20} + 426 q^{21} + 196 q^{22} - 692 q^{24}+ \cdots - 9682 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.5.g.a 28.g 28.g $28$ $2.894$ None 28.5.g.a \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$