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

• Label: 1386.2.bs
• Level: $1386$
• Weight: $2$
• Character orbit: 1386.bs
• Rep. character: $\chi_{1386}(811,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $160$
• Sturm bound: $576$

Defining parameters

Level:	$N$	$=$	$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1386.bs (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$77$
Character field:			$\Q(\zeta_{10})$
Sturm bound:			$576$

Dimensions

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

	Total	New	Old
Modular forms	1216	160	1056
Cusp forms	1088	160	928
Eisenstein series	128	0	128

Trace form

160 * q + 40 * q^4 + 10 * q^7 - 12 * q^11 + 2 * q^14 - 40 * q^16 + 4 * q^22 + 16 * q^23 + 12 * q^25 + 10 * q^28 - 20 * q^29 + 40 * q^35 + 40 * q^37 - 8 * q^44 + 24 * q^49 - 16 * q^53 + 8 * q^56 - 16 * q^58 + 40 * q^64 + 112 * q^67 - 4 * q^70 - 8 * q^71 + 40 * q^74 + 68 * q^77 + 60 * q^79 + 40 * q^85 + 28 * q^86 + 16 * q^88 - 20 * q^91 + 44 * q^92 - 60 * q^95

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}}(77, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(154, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(231, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(462, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(693, [\chi])$$^{\oplus 2}$