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

• Label: 1575.4.bc
• Level: $1575$
• Weight: $4$
• Character orbit: 1575.bc
• Rep. character: $\chi_{1575}(899,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $288$
• Sturm bound: $960$

Defining parameters

Level:	$N$	$=$	$1575 = 3^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1575.bc (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$105$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$960$

Dimensions

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

	Total	New	Old
Modular forms	1488	288	1200
Cusp forms	1392	288	1104
Eisenstein series	96	0	96

Trace form

$288 q - 576 q^{4} - 2304 q^{16} + 216 q^{19} + 1656 q^{31} - 1704 q^{46} + 3240 q^{49} - 1296 q^{61} + 20736 q^{64} + 504 q^{79} - 5832 q^{91} + 7056 q^{94}+O(q^{100})$

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