Space of modular forms of level 126, weight 9, and Character 126.o

• Label: 126.9.o
• Level: $126$
• Weight: $9$
• Character orbit: 126.o
• Rep. character: $\chi_{126}(13,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $128$
• Sturm bound: $216$

Defining parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(126, [\chi])\).

	Total	New	Old
Modular forms	392	128	264
Cusp forms	376	128	248
Eisenstein series	16	0	16

Trace form

\( 128 q - 8192 q^{4} + 1846 q^{7} - 12216 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{9}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)