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

• Label: 1224.2.bj
• Level: $1224$
• Weight: $2$
• Character orbit: 1224.bj
• Rep. character: $\chi_{1224}(205,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $384$
• Sturm bound: $432$

Defining parameters

Level:	$N$	$=$	$1224 = 2^{3} \cdot 3^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1224.bj (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$72$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$432$

Dimensions

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

	Total	New	Old
Modular forms	440	384	56
Cusp forms	424	384	40
Eisenstein series	16	0	16

Trace form

384 * q - 6 * q^6 + 12 * q^8 + 12 * q^12 - 22 * q^18 + 14 * q^20 + 24 * q^23 - 2 * q^24 + 192 * q^25 - 56 * q^26 - 56 * q^30 - 10 * q^32 - 40 * q^36 - 48 * q^38 - 24 * q^39 - 18 * q^42 - 108 * q^44 - 62 * q^48 - 192 * q^49 + 20 * q^50 - 18 * q^52 + 50 * q^54 - 68 * q^56 + 18 * q^58 - 22 * q^60 + 76 * q^62 - 36 * q^64 + 40 * q^66 - 112 * q^71 + 32 * q^72 + 42 * q^74 - 24 * q^78 + 44 * q^80 + 16 * q^81 - 36 * q^82 + 128 * q^84 - 26 * q^86 - 104 * q^87 - 24 * q^88 - 32 * q^89 - 26 * q^90 - 20 * q^92 + 6 * q^94 - 64 * q^95 + 90 * q^96 - 108 * 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}}(72, [\chi])$$^{\oplus 2}$