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

• Label: 1224.2.bs
• Level: $1224$
• Weight: $2$
• Character orbit: 1224.bs
• Rep. character: $\chi_{1224}(253,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $352$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.bs (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(432\)

Dimensions

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

	Total	New	Old
Modular forms	896	368	528
Cusp forms	832	352	480
Eisenstein series	64	16	48

Trace form

352 * q + 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^10 + 20 * q^14 - 8 * q^16 + 8 * q^17 + 20 * q^20 - 28 * q^22 + 8 * q^23 + 28 * q^26 + 36 * q^28 - 8 * q^31 - 36 * q^32 + 12 * q^34 + 16 * q^41 + 4 * q^44 + 4 * q^46 - 8 * q^49 + 48 * q^50 - 40 * q^52 + 52 * q^56 + 56 * q^58 + 12 * q^62 + 8 * q^65 + 52 * q^68 + 80 * q^70 + 72 * q^71 + 32 * q^73 - 28 * q^74 - 24 * q^76 - 8 * q^79 + 56 * q^80 + 64 * q^82 + 80 * q^86 + 8 * q^88 - 108 * q^92 + 88 * q^94 + 8 * q^95 - 8 * q^97

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

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