Space of modular forms of level 3744, weight 2, and Character 3744.dj

• Label: 3744.2.dj
• Level: $3744$
• Weight: $2$
• Character orbit: 3744.dj
• Rep. character: $\chi_{3744}(1535,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $288$
• Sturm bound: $1344$

Defining parameters

Level:	$N$	$=$	$3744 = 2^{5} \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3744.dj (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$36$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$1344$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3744, [\chi])$.

	Total	New	Old
Modular forms	1376	288	1088
Cusp forms	1312	288	1024
Eisenstein series	64	0	64

Trace form

$288 q + 8 q^{9} - 16 q^{21} + 144 q^{25} - 48 q^{29} + 40 q^{33} + 72 q^{41} + 16 q^{45} + 144 q^{49} + 40 q^{57} - 32 q^{69} - 48 q^{73} - 24 q^{81} + 96 q^{93} - 24 q^{97}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(3744, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(3744, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3744, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(36, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(144, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(288, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(468, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1872, [\chi])$$^{\oplus 2}$