Space of modular forms of level 2548, weight 2, and Character 2548.cf

• Label: 2548.2.cf
• Level: $2548$
• Weight: $2$
• Character orbit: 2548.cf
• Rep. character: $\chi_{2548}(655,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1088$
• Sturm bound: $784$

Defining parameters

Level:	$N$	$=$	$2548 = 2^{2} \cdot 7^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2548.cf (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$364$
Character field:			$\Q(\zeta_{12})$
Sturm bound:			$784$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(2548, [\chi])$.

	Total	New	Old
Modular forms	1632	1152	480
Cusp forms	1504	1088	416
Eisenstein series	128	64	64

Trace form

1088 * q + 2 * q^2 + 4 * q^5 + 16 * q^6 - 16 * q^8 + 520 * q^9 + 16 * q^13 + 4 * q^16 + 12 * q^18 + 40 * q^20 - 32 * q^22 - 16 * q^24 - 8 * q^26 - 64 * q^29 + 12 * q^32 + 28 * q^33 + 80 * q^34 + 12 * q^37 - 36 * q^40 + 26 * q^44 - 48 * q^45 + 48 * q^46 + 120 * q^48 - 24 * q^50 - 24 * q^52 + 22 * q^54 - 24 * q^57 + 54 * q^58 - 64 * q^60 + 16 * q^61 - 4 * q^65 - 28 * q^66 + 36 * q^68 - 62 * q^72 + 28 * q^73 + 116 * q^74 - 8 * q^76 - 24 * q^78 - 38 * q^80 - 432 * q^81 + 8 * q^85 - 22 * q^86 - 12 * q^89 + 48 * q^92 - 20 * q^93 - 20 * q^94 - 38 * q^96 - 80 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(2548, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(2548, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(2548, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(364, [\chi])$$^{\oplus 2}$