Space of modular forms of level 672, weight 4, and Character 672.bq

• Label: 672.4.bq
• Level: $672$
• Weight: $4$
• Character orbit: 672.bq
• Rep. character: $\chi_{672}(85,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $576$
• Sturm bound: $512$

Defining parameters

Level:	$N$	$=$	$672 = 2^{5} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	672.bq (of order $8$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$32$
Character field:			$\Q(\zeta_{8})$
Sturm bound:			$512$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(672, [\chi])$.

	Total	New	Old
Modular forms	1552	576	976
Cusp forms	1520	576	944
Eisenstein series	32	0	32

Trace form

576 * q + 240 * q^10 - 96 * q^12 - 120 * q^16 - 72 * q^18 + 392 * q^22 + 656 * q^23 + 912 * q^24 + 80 * q^26 + 2480 * q^32 + 2000 * q^34 - 3280 * q^40 + 1616 * q^43 - 1000 * q^44 - 2880 * q^46 - 2976 * q^51 - 1728 * q^52 + 1504 * q^53 - 432 * q^54 - 576 * q^55 + 392 * q^56 + 2448 * q^60 - 3648 * q^61 + 5856 * q^62 + 1008 * q^63 + 816 * q^67 + 10064 * q^68 - 2112 * q^69 + 1008 * q^70 - 2632 * q^74 - 4416 * q^75 - 10064 * q^76 + 3808 * q^77 - 12640 * q^80 - 11680 * q^82 - 4736 * q^86 + 3120 * q^88 + 2152 * q^92 + 23600 * q^94

Decomposition of $S_{4}^{\mathrm{new}}(672, [\chi])$ into newform subspaces

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

Decomposition of $S_{4}^{\mathrm{old}}(672, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(672, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(32, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(96, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(224, [\chi])$$^{\oplus 2}$