Space of modular forms of level 2160, weight 4, and Character 2160.eg

• Label: 2160.4.eg
• Level: $2160$
• Weight: $4$
• Character orbit: 2160.eg
• Rep. character: $\chi_{2160}(187,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $15504$
• Sturm bound: $1728$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2160.eg (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2160 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2160, [\chi])\).

	Total	New	Old
Modular forms	15600	15600	0
Cusp forms	15504	15504	0
Eisenstein series	96	96	0

Trace form

15504 * q - 12 * q^2 - 24 * q^3 - 12 * q^5 - 24 * q^6 - 24 * q^7 - 6 * q^8 - 6 * q^10 - 24 * q^11 - 12 * q^12 - 24 * q^16 - 12 * q^17 - 726 * q^18 - 12 * q^20 - 24 * q^21 - 12 * q^22 - 24 * q^23 + 324 * q^24 - 48 * q^26 - 24 * q^27 - 24 * q^28 + 150 * q^30 + 1368 * q^32 - 24 * q^33 - 6 * q^35 - 24 * q^36 - 60 * q^38 + 738 * q^40 + 408 * q^42 - 1776 * q^44 - 12 * q^45 - 12 * q^46 - 12 * q^48 - 12 * q^50 - 24 * q^51 - 12 * q^52 - 48 * q^53 - 48 * q^55 - 24 * q^56 + 324 * q^57 - 12 * q^58 + 1932 * q^60 - 24 * q^61 - 6 * q^62 - 24 * q^65 - 9912 * q^66 - 396 * q^68 - 60 * q^70 - 24 * q^71 + 3060 * q^72 - 96 * q^74 + 4944 * q^75 - 24 * q^76 - 24 * q^77 - 3690 * q^78 + 156 * q^80 - 48 * q^81 - 24 * q^82 - 24 * q^83 - 648 * q^84 - 762 * q^85 - 24 * q^86 - 24 * q^87 - 3084 * q^88 + 21078 * q^90 - 12 * q^91 + 9450 * q^92 - 5100 * q^96 - 24 * q^97 + 1932 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

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