Space of modular forms of level 2205, weight 4, and Character 2205.do

• Label: 2205.4.do
• Level: $2205$
• Weight: $4$
• Character orbit: 2205.do
• Rep. character: $\chi_{2205}(89,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $4032$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2205.do (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 735 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2205, [\chi])\).

	Total	New	Old
Modular forms	12192	4032	8160
Cusp forms	12000	4032	7968
Eisenstein series	192	0	192

Trace form

\( 4032 q + 1344 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)