Space of modular forms of level 810, weight 4, and Character 810.w

• Label: 810.4.w
• Level: $810$
• Weight: $4$
• Character orbit: 810.w
• Rep. character: $\chi_{810}(23,\cdot)$
• Character field: $\Q(\zeta_{108})$
• Dimension: $5832$
• Sturm bound: $648$

Defining parameters

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	810.w (of order \(108\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 405 \)
Character field:			\(\Q(\zeta_{108})\)
Sturm bound:			\(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(810, [\chi])\).

	Total	New	Old
Modular forms	17640	5832	11808
Cusp forms	17352	5832	11520
Eisenstein series	288	0	288

Trace form

\( 5832 q + 576 q^{20} - 1512 q^{30} + 4968 q^{35} + 3708 q^{41} - 10152 q^{51} + 11016 q^{67} + 1152 q^{72} + 39168 q^{77} + 21888 q^{87} - 7488 q^{92} + 3708 q^{93} + 20736 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(810, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(810, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)