Space of modular forms of level 1368, weight 3, and Character 1368.bd

• Label: 1368.3.bd
• Level: $1368$
• Weight: $3$
• Character orbit: 1368.bd
• Rep. character: $\chi_{1368}(107,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $320$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1368.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1368, [\chi])\).

	Total	New	Old
Modular forms	976	320	656
Cusp forms	944	320	624
Eisenstein series	32	0	32

Trace form

\( 320 q + 4 q^{4} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)