Space of modular forms of level 1680, weight 4, and Character 1680.bl

• Label: 1680.4.bl
• Level: $1680$
• Weight: $4$
• Character orbit: 1680.bl
• Rep. character: $\chi_{1680}(127,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $216$
• Sturm bound: $1536$

Defining parameters

Level:	$N$	$=$	$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1680.bl (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$20$
Character field:			$\Q(i)$
Sturm bound:			$1536$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(1680, [\chi])$.

	Total	New	Old
Modular forms	2352	216	2136
Cusp forms	2256	216	2040
Eisenstein series	96	0	96

Trace form

$216 q - 552 q^{13} + 312 q^{17} - 264 q^{25} - 792 q^{37} - 216 q^{45} + 3432 q^{53} + 3144 q^{65} - 888 q^{73} - 17496 q^{81} - 2664 q^{85} + 2736 q^{93} + 5448 q^{97}+O(q^{100})$

Decomposition of $S_{4}^{\mathrm{new}}(1680, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(1680, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(1680, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(20, [\chi])$$^{\oplus 12}$$\oplus$$S_{4}^{\mathrm{new}}(60, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(80, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(140, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(240, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(420, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(560, [\chi])$$^{\oplus 2}$