Space of modular forms of level 2005, weight 2, and Character 2005.by

• Label: 2005.2.by
• Level: $2005$
• Weight: $2$
• Character orbit: 2005.by
• Rep. character: $\chi_{2005}(12,\cdot)$
• Character field: $\Q(\zeta_{400})$
• Dimension: $31840$
• Sturm bound: $402$

Defining parameters

Level:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.by (of order \(400\) and degree \(160\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2005 \)
Character field:			\(\Q(\zeta_{400})\)
Sturm bound:			\(402\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2005, [\chi])\).

	Total	New	Old
Modular forms	32480	32480	0
Cusp forms	31840	31840	0
Eisenstein series	640	640	0

Trace form

\( 31840 q - 160 q^{2} - 160 q^{3} - 160 q^{5} - 320 q^{6} - 160 q^{7} - 160 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2005, [\chi])\) into newform subspaces

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