Space of modular forms of level 2160, weight 2, and Character 2160.cr

• Label: 2160.2.cr
• Level: $2160$
• Weight: $2$
• Character orbit: 2160.cr
• Rep. character: $\chi_{2160}(197,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $560$
• Sturm bound: $864$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2160.cr (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 720 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2160, [\chi])\).

	Total	New	Old
Modular forms	1776	592	1184
Cusp forms	1680	560	1120
Eisenstein series	96	32	64

Trace form

560 * q + 6 * q^2 + 6 * q^5 + 12 * q^11 - 4 * q^16 + 6 * q^20 + 6 * q^22 + 8 * q^28 - 8 * q^31 - 54 * q^32 - 12 * q^34 + 18 * q^38 + 8 * q^40 - 4 * q^43 - 40 * q^46 + 12 * q^47 + 6 * q^50 - 18 * q^52 + 12 * q^56 - 10 * q^58 - 4 * q^61 - 24 * q^64 + 12 * q^65 - 4 * q^67 + 30 * q^68 + 2 * q^70 - 24 * q^74 + 8 * q^76 + 12 * q^77 - 12 * q^85 + 12 * q^86 - 10 * q^88 - 16 * q^91 + 120 * q^92 + 12 * q^95 - 4 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)