Space of modular forms of level 4400, weight 2, and Character 4400.fw

• Label: 4400.2.fw
• Level: $4400$
• Weight: $2$
• Character orbit: 4400.fw
• Rep. character: $\chi_{4400}(293,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $3424$
• Sturm bound: $1440$

Defining parameters

Level:	$N$	$=$	$4400 = 2^{4} \cdot 5^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4400.fw (of order $20$ and degree $8$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$880$
Character field:			$\Q(\zeta_{20})$
Sturm bound:			$1440$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(4400, [\chi])$.

	Total	New	Old
Modular forms	5856	3488	2368
Cusp forms	5664	3424	2240
Eisenstein series	192	64	128

Decomposition of $S_{2}^{\mathrm{new}}(4400, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(4400, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(4400, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(880, [\chi])$$^{\oplus 2}$