Space of modular forms of level 3528, weight 2, and Character 3528.fm

• Label: 3528.2.fm
• Level: $3528$
• Weight: $2$
• Character orbit: 3528.fm
• Rep. character: $\chi_{3528}(17,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $672$
• Sturm bound: $1344$

Defining parameters

Level:	$N$	$=$	$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3528.fm (of order $42$ and degree $12$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$147$
Character field:			$\Q(\zeta_{42})$
Sturm bound:			$1344$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3528, [\chi])$.

	Total	New	Old
Modular forms	8256	672	7584
Cusp forms	7872	672	7200
Eisenstein series	384	0	384

Trace form

$672 q + 8 q^{7} - 12 q^{19} + 44 q^{25} - 24 q^{31} - 40 q^{37} + 8 q^{43} - 32 q^{49} - 28 q^{55} - 28 q^{61} + 20 q^{67} + 60 q^{73} + 32 q^{79} + 80 q^{85} + 28 q^{91}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(3528, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(3528, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3528, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(147, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(294, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(441, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(588, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(882, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(1176, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1764, [\chi])$$^{\oplus 2}$