Space of modular forms of level 3780, weight 2, and Character 3780.dk

• Label: 3780.2.dk
• Level: $3780$
• Weight: $2$
• Character orbit: 3780.dk
• Rep. character: $\chi_{3780}(421,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $432$
• Sturm bound: $1728$

Defining parameters

Level:	$N$	$=$	$3780 = 2^{2} \cdot 3^{3} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3780.dk (of order $9$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$27$
Character field:			$\Q(\zeta_{9})$
Sturm bound:			$1728$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3780, [\chi])$.

	Total	New	Old
Modular forms	5256	432	4824
Cusp forms	5112	432	4680
Eisenstein series	144	0	144

Trace form

432 * q + 6 * q^9 - 6 * q^11 - 84 * q^27 - 72 * q^29 - 12 * q^33 - 12 * q^35 - 12 * q^39 + 12 * q^41 - 36 * q^43 + 48 * q^51 + 144 * q^53 + 156 * q^57 + 24 * q^59 - 12 * q^65 - 36 * q^67 - 48 * q^69 - 24 * q^71 - 36 * q^79 - 138 * q^81 - 60 * q^83 - 36 * q^85 + 12 * q^89 + 12 * q^93 - 48 * q^95 - 36 * q^97 + 24 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(3780, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(3780, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3780, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(27, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(54, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(108, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(135, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(189, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(270, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(378, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(540, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(756, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(945, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(1890, [\chi])$$^{\oplus 2}$