Properties

Label 112.5.l
Level $112$
Weight $5$
Character orbit 112.l
Rep. character $\chi_{112}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $124$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 112.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 132 132 0
Cusp forms 124 124 0
Eisenstein series 8 8 0

Trace form

\( 124 q - 4 q^{2} - 10 q^{4} + 176 q^{8} - 100 q^{11} + 246 q^{14} - 8 q^{15} + 306 q^{16} - 1850 q^{18} - 164 q^{21} + 362 q^{22} + 960 q^{28} - 868 q^{29} + 1112 q^{30} - 3064 q^{32} + 1340 q^{35} - 3680 q^{36}+ \cdots + 39524 q^{99}+O(q^{100}) \) 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.l.a 112.l 112.l $4$ $11.577$ \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) 112.5.l.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{2}q^{2}+(2^{4}+\beta _{3})q^{4}+7^{2}\beta _{1}q^{7}+\cdots\)
112.5.l.b 112.l 112.l $120$ $11.577$ None 112.5.l.b \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$