Space of modular forms of level 387, weight 8, and Character 387.v

• Label: 387.8.v
• Level: $387$
• Weight: $8$
• Character orbit: 387.v
• Rep. character: $\chi_{387}(8,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $624$
• Sturm bound: $352$

Defining parameters

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	387.v (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 129 \)
Character field:			\(\Q(\zeta_{14})\)
Sturm bound:			\(352\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(387, [\chi])\).

	Total	New	Old
Modular forms	1872	624	1248
Cusp forms	1824	624	1200
Eisenstein series	48	0	48

Trace form

\( 624 q - 6912 q^{4} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(387, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)