Space of modular forms of level 1224, weight 4, and Character 1224.ck

• Label: 1224.4.ck
• Level: $1224$
• Weight: $4$
• Character orbit: 1224.ck
• Rep. character: $\chi_{1224}(125,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $1728$
• Sturm bound: $864$

Defining parameters

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1224.ck (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 408 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1224, [\chi])\).

	Total	New	Old
Modular forms	5248	1728	3520
Cusp forms	5120	1728	3392
Eisenstein series	128	0	128

Trace form

\( 1728 q + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)