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Properties

Label 44.4.g
Level $44$
Weight $4$
Character orbit 44.g
Rep. character $\chi_{44}(7,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $64$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 44.g (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(44, [\chi])\).

Total New Old
Modular forms 80 80 0
Cusp forms 64 64 0
Eisenstein series 16 16 0

Trace form

\( 64 q - 5 q^{2} + 7 q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} + 122 q^{9} - 38 q^{12} - 10 q^{13} + 66 q^{14} - 73 q^{16} - 10 q^{17} - 230 q^{18} - 180 q^{20} - 747 q^{22} - 455 q^{24} - 374 q^{25} + 330 q^{26}+ \cdots + 3904 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(44, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
44.4.g.a 44.g 44.g $64$ $2.596$ None 44.4.g.a \(-5\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{10}]$