Space of modular forms of level 7800, weight 2, and Character 7800.ds

• Label: 7800.2.ds
• Level: $7800$
• Weight: $2$
• Character orbit: 7800.ds
• Rep. character: $\chi_{7800}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $248$
• Sturm bound: $3360$

Defining parameters

Level:	$N$	$=$	$7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	7800.ds (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$65$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$3360$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(7800, [\chi])$.

	Total	New	Old
Modular forms	3456	248	3208
Cusp forms	3264	248	3016
Eisenstein series	192	0	192

Decomposition of $S_{2}^{\mathrm{new}}(7800, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(7800, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(7800, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(65, [\chi])$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(130, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(195, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(260, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(325, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(390, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(520, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(650, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(780, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(975, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1300, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1560, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1950, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(2600, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(3900, [\chi])$$^{\oplus 2}$