Space of modular forms of level 29760, weight 2, and Character 29760.cs

• Label: 29760.2.cs
• Level: $29760$
• Weight: $2$
• Character orbit: 29760.cs
• Rep. character: $\chi_{29760}(4897,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $1536$
• Sturm bound: $12288$

Defining parameters

Level:	$N$	$=$	$29760 = 2^{6} \cdot 3 \cdot 5 \cdot 31$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	29760.cs (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$1240$
Character field:			$\Q(i)$
Sturm bound:			$12288$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(29760, [\chi])$.

	Total	New	Old
Modular forms	12384	1536	10848
Cusp forms	12192	1536	10656
Eisenstein series	192	0	192

Decomposition of $S_{2}^{\mathrm{new}}(29760, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(29760, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(29760, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(1240, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(3720, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(4960, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(9920, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(14880, [\chi])$$^{\oplus 2}$