Space of modular forms of level 3000, weight 2, and Character 3000.be

• Label: 3000.2.be
• Level: $3000$
• Weight: $2$
• Character orbit: 3000.be
• Rep. character: $\chi_{3000}(349,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $720$
• Sturm bound: $1200$

Defining parameters

Level:	$N$	$=$	$3000 = 2^{3} \cdot 3 \cdot 5^{3}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3000.be (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$200$
Character field:			$\Q(\zeta_{10})$
Sturm bound:			$1200$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3000, [\chi])$.

	Total	New	Old
Modular forms	2480	720	1760
Cusp forms	2320	720	1600
Eisenstein series	160	0	160

Trace form

720 * q + 30 * q^8 - 180 * q^9 - 12 * q^14 - 12 * q^16 - 50 * q^22 - 20 * q^26 - 24 * q^31 + 16 * q^34 + 30 * q^38 - 16 * q^39 - 8 * q^41 - 42 * q^44 + 20 * q^46 - 720 * q^49 - 140 * q^52 + 36 * q^56 + 10 * q^58 + 50 * q^62 - 42 * q^64 + 8 * q^66 - 30 * q^72 + 44 * q^74 + 8 * q^76 + 40 * q^79 - 180 * q^81 + 24 * q^84 - 60 * q^86 + 170 * q^88 + 60 * q^89 + 190 * q^92 + 70 * q^94 + 60 * q^96 - 40 * q^97 + 140 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(3000, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(3000, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3000, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(200, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(600, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1000, [\chi])$$^{\oplus 2}$