Space of modular forms of level 1710, weight 2, and Character 1710.bd

• Label: 1710.2.bd
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.bd
• Rep. character: $\chi_{1710}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $240$
• Sturm bound: $720$

Defining parameters

Level:	$N$	$=$	$1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1710.bd (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$855$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$720$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(1710, [\chi])$.

	Total	New	Old
Modular forms	736	240	496
Cusp forms	704	240	464
Eisenstein series	32	0	32

Trace form

240 * q - 240 * q^4 - 16 * q^14 + 2 * q^15 + 240 * q^16 + 24 * q^21 - 24 * q^29 - 10 * q^30 + 12 * q^35 + 24 * q^39 + 48 * q^41 - 48 * q^45 + 120 * q^49 + 20 * q^50 + 60 * q^51 - 36 * q^54 + 16 * q^56 - 28 * q^59 - 2 * q^60 - 240 * q^64 - 38 * q^65 + 16 * q^66 + 8 * q^69 + 12 * q^71 + 32 * q^74 + 20 * q^75 + 72 * q^81 - 24 * q^84 - 128 * q^86 - 48 * q^89 - 12 * q^90 + 12 * q^95 + 4 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(1710, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(1710, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(1710, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(855, [\chi])$$^{\oplus 2}$