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Properties

Label 126.3.i
Level $126$
Weight $3$
Character orbit 126.i
Rep. character $\chi_{126}(65,\cdot)$
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.i (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

\( 32 q + 32 q^{4} + 8 q^{6} + 2 q^{7} + 4 q^{9} + 10 q^{13} + 36 q^{14} + 10 q^{15} - 64 q^{16} + 54 q^{17} + 24 q^{18} + 28 q^{19} + 16 q^{21} + 8 q^{24} - 160 q^{25} + 72 q^{26} - 126 q^{27} - 4 q^{28}+ \cdots + 394 q^{99}+O(q^{100}) \) 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.i.a 126.i 63.n $32$ $3.433$ None 126.3.i.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$

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

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