Properties

Label 112.5.x
Level $112$
Weight $5$
Character orbit 112.x
Rep. character $\chi_{112}(5,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $248$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 112.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(112, [\chi])\).

Total New Old
Modular forms 264 264 0
Cusp forms 248 248 0
Eisenstein series 16 16 0

Trace form

\( 248 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - 6 q^{5} - 188 q^{8} + 588 q^{10} + 94 q^{11} - 6 q^{12} + 396 q^{14} - 16 q^{15} - 312 q^{16} - 12 q^{17} + 194 q^{18} - 6 q^{19} + 158 q^{21} - 2372 q^{22} - 6 q^{24}+ \cdots - 656 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.5.x.a 112.x 112.x $248$ $11.577$ None 112.5.x.a \(-2\) \(-6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{12}]$