Space of modular forms of level 8800, weight 2, and Character 8800.bd

• Label: 8800.2.bd
• Level: $8800$
• Weight: $2$
• Character orbit: 8800.bd
• Rep. character: $\chi_{8800}(4993,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $432$
• Sturm bound: $2880$

Defining parameters

Level:	$N$	$=$	$8800 = 2^{5} \cdot 5^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	8800.bd (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$55$
Character field:			$\Q(i)$
Sturm bound:			$2880$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(8800, [\chi])$.

	Total	New	Old
Modular forms	2976	432	2544
Cusp forms	2784	432	2352
Eisenstein series	192	0	192

Decomposition of $S_{2}^{\mathrm{new}}(8800, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(8800, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(8800, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(55, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(110, [\chi])$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(220, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(275, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(440, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(550, [\chi])$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(880, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1100, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1760, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(2200, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(4400, [\chi])$$^{\oplus 2}$