Space of modular forms of level 10800, weight 2, and Character 10800.dl

• Label: 10800.2.dl
• Level: $10800$
• Weight: $2$
• Character orbit: 10800.dl
• Rep. character: $\chi_{10800}(4193,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $424$
• Sturm bound: $4320$

Defining parameters

Level:	$N$	$=$	$10800 = 2^{4} \cdot 3^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	10800.dl (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$45$
Character field:			$\Q(\zeta_{12})$
Sturm bound:			$4320$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(10800, [\chi])$.

	Total	New	Old
Modular forms	9072	440	8632
Cusp forms	8208	424	7784
Eisenstein series	864	16	848

Decomposition of $S_{2}^{\mathrm{new}}(10800, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(10800, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(10800, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(45, [\chi])$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(90, [\chi])$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(135, [\chi])$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(180, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(225, [\chi])$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(270, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(360, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(450, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(540, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(675, [\chi])$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(720, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(900, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(1080, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1350, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1800, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(2160, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(2700, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(3600, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(5400, [\chi])$$^{\oplus 2}$