Properties

Label 126.4.t
Level $126$
Weight $4$
Character orbit 126.t
Rep. character $\chi_{126}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(126, [\chi])\).

Total New Old
Modular forms 152 48 104
Cusp forms 136 48 88
Eisenstein series 16 0 16

Trace form

\( 48 q + 96 q^{4} - 12 q^{7} + 18 q^{9} - 72 q^{13} - 132 q^{14} + 132 q^{15} - 384 q^{16} - 144 q^{17} - 72 q^{18} + 270 q^{21} + 48 q^{24} + 1200 q^{25} - 120 q^{26} + 450 q^{27} + 48 q^{28} + 42 q^{29}+ \cdots - 5076 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.4.t.a 126.t 63.s $48$ $7.434$ None 126.4.l.a \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)