Space of modular forms of level 1386, weight 2, and Character 1386.bf

• Label: 1386.2.bf
• Level: $1386$
• Weight: $2$
• Character orbit: 1386.bf
• Rep. character: $\chi_{1386}(769,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $192$
• Sturm bound: $576$

Defining parameters

Level:	$N$	$=$	$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1386.bf (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$693$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$576$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(1386, [\chi])$.

	Total	New	Old
Modular forms	592	192	400
Cusp forms	560	192	368
Eisenstein series	32	0	32

Trace form

192 * q + 96 * q^4 - 16 * q^9 - 4 * q^11 + 8 * q^15 - 96 * q^16 + 24 * q^23 + 96 * q^25 - 8 * q^36 - 24 * q^42 - 8 * q^44 - 128 * q^53 + 24 * q^58 - 8 * q^60 - 192 * q^64 - 12 * q^70 - 48 * q^71 - 34 * q^77 - 16 * q^78 - 24 * q^81 - 8 * q^86 - 24 * q^92 - 48 * q^93 + 16 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(1386, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(1386, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(1386, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(693, [\chi])$$^{\oplus 2}$