Space of modular forms of level 1224, weight 2, and Character 1224.cj

• Label: 1224.2.cj
• Level: $1224$
• Weight: $2$
• Character orbit: 1224.cj
• Rep. character: $\chi_{1224}(91,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $704$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.cj (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1224, [\chi])\).

	Total	New	Old
Modular forms	1792	736	1056
Cusp forms	1664	704	960
Eisenstein series	128	32	96

Trace form

704 * q + 8 * q^2 - 8 * q^4 + 8 * q^8 - 8 * q^10 + 16 * q^11 + 8 * q^14 + 16 * q^17 - 16 * q^19 + 8 * q^20 - 8 * q^22 - 16 * q^25 - 24 * q^26 - 56 * q^28 + 48 * q^32 - 40 * q^34 + 32 * q^35 - 32 * q^38 - 72 * q^40 + 16 * q^41 - 16 * q^43 + 40 * q^44 + 8 * q^46 - 16 * q^49 - 16 * q^52 + 48 * q^56 + 48 * q^58 + 16 * q^59 + 64 * q^62 + 40 * q^64 + 96 * q^65 + 96 * q^68 + 64 * q^70 - 96 * q^73 + 56 * q^74 + 48 * q^76 + 104 * q^80 + 32 * q^82 + 16 * q^83 - 64 * q^86 + 56 * q^88 + 16 * q^89 - 16 * q^91 + 120 * q^92 - 104 * q^94 - 16 * q^97 - 128 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1224, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)