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

• Label: 1575.4.bx
• Level: $1575$
• Weight: $4$
• Character orbit: 1575.bx
• Rep. character: $\chi_{1575}(64,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $904$
• Sturm bound: $960$

Defining parameters

Level:	$N$	$=$	$1575 = 3^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1575.bx (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$25$
Character field:			$\Q(\zeta_{10})$
Sturm bound:			$960$

Dimensions

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

	Total	New	Old
Modular forms	2912	904	2008
Cusp forms	2848	904	1944
Eisenstein series	64	0	64

Trace form

904 * q + 912 * q^4 + 18 * q^5 - 104 * q^10 + 88 * q^11 - 56 * q^14 - 3496 * q^16 - 72 * q^19 - 168 * q^20 + 1010 * q^22 - 220 * q^23 - 298 * q^25 + 348 * q^26 - 928 * q^29 - 72 * q^31 + 168 * q^34 + 28 * q^35 + 1030 * q^37 + 3010 * q^38 - 66 * q^40 + 596 * q^41 - 1678 * q^44 + 280 * q^46 - 3620 * q^47 - 44296 * q^49 + 426 * q^50 - 3010 * q^53 - 1556 * q^55 + 672 * q^56 - 1810 * q^58 - 588 * q^59 - 1460 * q^61 + 5350 * q^62 + 12696 * q^64 + 1938 * q^65 - 2340 * q^67 + 756 * q^70 - 316 * q^71 + 2880 * q^73 + 11316 * q^74 + 2212 * q^76 + 560 * q^77 + 2292 * q^79 + 3512 * q^80 + 2460 * q^83 + 2246 * q^85 + 2600 * q^86 - 10620 * q^88 - 1082 * q^89 - 728 * q^91 - 10460 * q^92 - 5120 * q^94 - 3188 * q^95 + 2640 * q^97

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}}(25, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(75, [\chi])$$^{\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}}(525, [\chi])$$^{\oplus 2}$