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Properties

Label 126.3.o
Level $126$
Weight $3$
Character orbit 126.o
Rep. character $\chi_{126}(13,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(126, [\chi])\).

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.o.a 126.o 63.l $32$ $3.433$ None 126.3.o.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)