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Properties

Label 132.3.k
Level $132$
Weight $3$
Character orbit 132.k
Rep. character $\chi_{132}(31,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $96$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 132.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(132, [\chi])\).

Total New Old
Modular forms 208 96 112
Cusp forms 176 96 80
Eisenstein series 32 0 32

Trace form

\( 96 q + 4 q^{2} + 12 q^{4} - 20 q^{8} + 72 q^{9} + 8 q^{10} + 24 q^{12} + 50 q^{14} + 80 q^{16} + 18 q^{18} - 10 q^{20} - 54 q^{22} - 54 q^{24} - 136 q^{25} - 206 q^{26} - 102 q^{28} + 64 q^{29} - 108 q^{30}+ \cdots + 1768 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(132, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
132.3.k.a 132.k 44.h $96$ $3.597$ None 132.3.k.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(132, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(132, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)