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

• Label: 1575.4.p
• Level: $1575$
• Weight: $4$
• Character orbit: 1575.p
• Rep. character: $\chi_{1575}(118,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $356$
• Sturm bound: $960$

Defining parameters

Level:	$N$	$=$	$1575 = 3^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1575.p (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$35$
Character field:			$\Q(i)$
Sturm bound:			$960$

Dimensions

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

	Total	New	Old
Modular forms	1488	364	1124
Cusp forms	1392	356	1036
Eisenstein series	96	8	88

Trace form

356 * q - 4 * q^2 - 14 * q^7 - 56 * q^8 + 136 * q^11 - 5288 * q^16 + 228 * q^22 + 92 * q^23 - 48 * q^28 - 912 * q^32 - 548 * q^37 + 100 * q^43 + 4020 * q^46 - 308 * q^53 + 4444 * q^56 - 3092 * q^58 + 636 * q^67 - 744 * q^71 - 1672 * q^77 - 9036 * q^86 + 560 * q^88 - 7180 * q^91 + 4272 * q^92 + 204 * q^98

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}}(35, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(105, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(175, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(315, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(525, [\chi])$$^{\oplus 2}$