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Properties

Label 126.7.o
Level $126$
Weight $7$
Character orbit 126.o
Rep. character $\chi_{126}(13,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(126, [\chi])\).

Total New Old
Modular forms 296 96 200
Cusp forms 280 96 184
Eisenstein series 16 0 16

Trace form

\( 96 q - 1536 q^{4} - 240 q^{7} + 432 q^{9} - 576 q^{11} + 1584 q^{14} + 10608 q^{15} - 49152 q^{16} + 9984 q^{18} + 4500 q^{21} + 40536 q^{23} + 150000 q^{25} + 15360 q^{28} + 13896 q^{29} - 99168 q^{30}+ \cdots - 2509920 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{7}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.7.o.a 126.o 63.l $96$ $28.987$ None 126.7.o.a \(0\) \(0\) \(0\) \(-240\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{7}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)