Space of modular forms of level 1575, weight 4, and Character 1575.d

• Label: 1575.4.d
• Level: $1575$
• Weight: $4$
• Character orbit: 1575.d
• Rep. character: $\chi_{1575}(1324,\cdot)$
• Character field: $\Q$
• Dimension: $134$
• Sturm bound: $960$

Defining parameters

Level:	$N$	$=$	$1575 = 3^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1575.d (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Sturm bound:			$960$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(1575, [\chi])$.

	Total	New	Old
Modular forms	744	134	610
Cusp forms	696	134	562
Eisenstein series	48	0	48

Trace form

134 * q - 504 * q^4 + 80 * q^11 - 56 * q^14 + 1976 * q^16 + 96 * q^19 - 636 * q^26 - 836 * q^29 + 24 * q^31 - 1088 * q^34 + 544 * q^41 - 1146 * q^44 + 202 * q^46 - 6566 * q^49 + 630 * q^56 - 20 * q^59 + 232 * q^61 - 7230 * q^64 + 5204 * q^71 - 390 * q^74 + 4188 * q^76 - 5836 * q^79 - 1026 * q^86 - 2304 * q^89 - 224 * q^91 - 10508 * q^94

Decomposition of $S_{4}^{\mathrm{new}}(1575, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(1575, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(1575, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(15, [\chi])$$^{\oplus 8}$$\oplus$$S_{4}^{\mathrm{new}}(25, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(35, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(45, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(75, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(105, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(175, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(225, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(315, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(525, [\chi])$$^{\oplus 2}$