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Properties

Label 126.6.t
Level $126$
Weight $6$
Character orbit 126.t
Rep. character $\chi_{126}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 126.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(126, [\chi])\).

Total New Old
Modular forms 248 80 168
Cusp forms 232 80 152
Eisenstein series 16 0 16

Trace form

\( 80 q + 640 q^{4} + 58 q^{7} - 30 q^{9} + 1086 q^{13} + 120 q^{14} - 474 q^{15} - 10240 q^{16} - 1602 q^{17} - 1776 q^{18} + 2214 q^{21} + 1920 q^{24} + 50000 q^{25} + 10032 q^{26} + 4500 q^{27} - 928 q^{28}+ \cdots + 76770 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.6.t.a 126.t 63.s $80$ $20.208$ None 126.6.l.a \(0\) \(0\) \(0\) \(58\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{6}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)