Space of modular forms of level 147, weight 10, and Character 147.o

• Label: 147.10.o
• Level: $147$
• Weight: $10$
• Character orbit: 147.o
• Rep. character: $\chi_{147}(5,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1992$
• Sturm bound: $186$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	147.o (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(186\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(147, [\chi])\).

	Total	New	Old
Modular forms	2040	2040	0
Cusp forms	1992	1992	0
Eisenstein series	48	48	0

Trace form

\( 1992 q - 11 q^{3} - 42010 q^{4} + 15890 q^{6} + 7476 q^{7} - 135197 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

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