Space of modular forms of level 2100, weight 3, and Character 2100.bf

• Label: 2100.3.bf
• Level: $2100$
• Weight: $3$
• Character orbit: 2100.bf
• Rep. character: $\chi_{2100}(299,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $1136$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 420 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2100, [\chi])\).

	Total	New	Old
Modular forms	1968	1168	800
Cusp forms	1872	1136	736
Eisenstein series	96	32	64

Trace form

\( 1136 q + 4 q^{4} + 4 q^{9} - 4 q^{16} + 12 q^{21} + 60 q^{24} - 144 q^{36} + 128 q^{46} - 64 q^{49} - 102 q^{54} - 24 q^{61} - 176 q^{64} + 264 q^{66} - 84 q^{81} - 98 q^{84} - 780 q^{94} + 1086 q^{96}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)