Space of modular forms of level 3150, weight 2, and Character 3150.db

• Label: 3150.2.db
• Level: $3150$
• Weight: $2$
• Character orbit: 3150.db
• Rep. character: $\chi_{3150}(89,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $640$
• Sturm bound: $1440$

Defining parameters

Level:	$N$	$=$	$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3150.db (of order $30$ and degree $8$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$525$
Character field:			$\Q(\zeta_{30})$
Sturm bound:			$1440$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3150, [\chi])$.

	Total	New	Old
Modular forms	5888	640	5248
Cusp forms	5632	640	4992
Eisenstein series	256	0	256

Trace form

640 * q + 80 * q^4 - 12 * q^10 + 80 * q^16 - 80 * q^22 + 12 * q^25 - 20 * q^28 + 36 * q^31 + 12 * q^40 - 24 * q^46 + 8 * q^49 - 160 * q^64 - 12 * q^70 - 240 * q^73 - 8 * q^79 - 48 * q^85 + 20 * q^88 + 104 * q^91 + 96 * q^94

Decomposition of $S_{2}^{\mathrm{new}}(3150, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(3150, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3150, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(525, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1050, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1575, [\chi])$$^{\oplus 2}$