Space of modular forms of level 1920, weight 2, and Character 1920.bs

• Label: 1920.2.bs
• Level: $1920$
• Weight: $2$
• Character orbit: 1920.bs
• Rep. character: $\chi_{1920}(239,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $368$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bs (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 480 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1920, [\chi])\).

	Total	New	Old
Modular forms	1600	400	1200
Cusp forms	1472	368	1104
Eisenstein series	128	32	96

Trace form

\( 368 q - 8 q^{9} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 8 q^{25} + 8 q^{39} - 4 q^{45} - 16 q^{51} + 40 q^{55} - 48 q^{61} - 8 q^{69} + 4 q^{75} + 64 q^{79} + 32 q^{85} + 16 q^{91} + 72 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1920, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 3}\)