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

• Label: 3744.2.gq
• Level: $3744$
• Weight: $2$
• Character orbit: 3744.gq
• Rep. character: $\chi_{3744}(175,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $656$
• Sturm bound: $1344$

Defining parameters

Level:	$N$	$=$	$3744 = 2^{5} \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3744.gq (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$936$
Character field:			$\Q(\zeta_{12})$
Sturm bound:			$1344$

Dimensions

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

	Total	New	Old
Modular forms	2752	688	2064
Cusp forms	2624	656	1968
Eisenstein series	128	32	96

Trace form

656 * q + 4 * q^3 - 4 * q^9 + 4 * q^11 - 24 * q^17 + 16 * q^19 + 16 * q^27 - 32 * q^33 + 8 * q^35 - 4 * q^41 + 12 * q^43 - 12 * q^49 + 4 * q^57 + 52 * q^59 - 4 * q^65 + 4 * q^67 - 16 * q^73 + 48 * q^75 - 4 * q^81 + 4 * q^83 - 16 * q^89 + 16 * q^91 - 4 * q^97 + 36 * q^99

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}}(936, [\chi])$$^{\oplus 3}$