Space of modular forms of level 1680, weight 2, and Character 1680.fi

• Label: 1680.2.fi
• Level: $1680$
• Weight: $2$
• Character orbit: 1680.fi
• Rep. character: $\chi_{1680}(451,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $512$
• Sturm bound: $768$

Defining parameters

Level:	$N$	$=$	$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1680.fi (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$112$
Character field:			$\Q(\zeta_{12})$
Sturm bound:			$768$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(1680, [\chi])$.

	Total	New	Old
Modular forms	1568	512	1056
Cusp forms	1504	512	992
Eisenstein series	64	0	64

Trace form

512 * q - 8 * q^4 + 16 * q^11 + 32 * q^14 + 8 * q^16 - 8 * q^18 - 32 * q^22 - 32 * q^23 + 64 * q^28 - 64 * q^29 + 32 * q^37 + 32 * q^43 + 8 * q^44 + 40 * q^46 + 16 * q^50 + 72 * q^52 + 32 * q^53 + 112 * q^56 + 48 * q^58 + 96 * q^59 - 32 * q^64 + 72 * q^66 + 16 * q^67 + 120 * q^68 + 32 * q^70 - 128 * q^71 + 8 * q^72 + 8 * q^74 - 48 * q^78 + 256 * q^81 - 48 * q^84 + 104 * q^86 + 8 * q^88 - 16 * q^91 - 256 * q^92 - 72 * q^94 - 184 * q^98 + 32 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(1680, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(1680, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(1680, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(112, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(336, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(560, [\chi])$$^{\oplus 2}$