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

• Label: 3528.2.eq
• Level: $3528$
• Weight: $2$
• Character orbit: 3528.eq
• Rep. character: $\chi_{3528}(269,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $2688$
• Sturm bound: $1344$

Defining parameters

Level:	$N$	$=$	$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3528.eq (of order $42$ and degree $12$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$1176$
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	8160	2688	5472
Cusp forms	7968	2688	5280
Eisenstein series	192	0	192

Trace form

$2688 q + 24 q^{22} - 224 q^{25} + 40 q^{28} - 112 q^{34} - 172 q^{40} + 20 q^{46} - 16 q^{49} - 36 q^{52} + 16 q^{58} + 72 q^{64} + 200 q^{70} - 48 q^{73} + 84 q^{76} - 8 q^{82} + 24 q^{88} + 276 q^{94}+O(q^{100})$

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}}(1176, [\chi])$$^{\oplus 2}$