Space of modular forms of level 2600, weight 2, and Character 2600.bm

• Label: 2600.2.bm
• Level: $2600$
• Weight: $2$
• Character orbit: 2600.bm
• Rep. character: $\chi_{2600}(1451,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $520$
• Sturm bound: $840$

Defining parameters

Level:	$N$	$=$	$2600 = 2^{3} \cdot 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2600.bm (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$104$
Character field:			$\Q(i)$
Sturm bound:			$840$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(2600, [\chi])$.

	Total	New	Old
Modular forms	864	544	320
Cusp forms	816	520	296
Eisenstein series	48	24	24

Trace form

520 * q + 2 * q^2 + 8 * q^3 + 4 * q^6 + 8 * q^8 + 504 * q^9 - 12 * q^11 + 20 * q^14 - 20 * q^16 + 6 * q^18 + 4 * q^19 + 16 * q^22 - 44 * q^24 - 6 * q^26 + 32 * q^27 + 32 * q^28 - 8 * q^32 + 16 * q^33 + 44 * q^34 - 16 * q^41 + 60 * q^42 - 20 * q^44 - 16 * q^46 + 28 * q^48 + 20 * q^52 - 8 * q^54 + 32 * q^57 + 56 * q^58 - 4 * q^59 + 64 * q^66 + 4 * q^67 + 28 * q^68 - 12 * q^72 - 32 * q^73 + 48 * q^74 - 12 * q^76 - 40 * q^78 + 424 * q^81 - 36 * q^83 - 76 * q^84 + 76 * q^86 + 24 * q^89 - 92 * q^91 - 48 * q^92 + 92 * q^94 - 12 * q^96 - 16 * q^97 - 54 * q^98 - 60 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(2600, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(2600, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(2600, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(104, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(520, [\chi])$$^{\oplus 2}$