Space of modular forms of level 1764, weight 4, and Character 1764.w

• Label: 1764.4.w
• Level: $1764$
• Weight: $4$
• Character orbit: 1764.w
• Rep. character: $\chi_{1764}(509,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $240$
• Sturm bound: $1344$

Defining parameters

Level:	$N$	$=$	$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1764.w (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$63$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$1344$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(1764, [\chi])$.

	Total	New	Old
Modular forms	2064	240	1824
Cusp forms	1968	240	1728
Eisenstein series	96	0	96

Trace form

240 * q + 4 * q^9 - 24 * q^11 + 36 * q^13 - 174 * q^15 + 72 * q^17 - 186 * q^23 - 3000 * q^25 + 396 * q^27 - 42 * q^29 - 84 * q^37 + 1400 * q^39 + 618 * q^41 + 42 * q^43 - 366 * q^45 - 396 * q^47 + 678 * q^51 + 2148 * q^53 - 536 * q^57 - 1500 * q^59 + 588 * q^67 + 924 * q^69 - 564 * q^75 - 2544 * q^79 - 3924 * q^81 + 720 * q^85 - 2640 * q^87 - 1722 * q^89 + 612 * q^93 + 792 * q^97 - 3574 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(1764, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(1764, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(1764, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(63, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(126, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(252, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(441, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(882, [\chi])$$^{\oplus 2}$