Space of modular forms of level 1584, weight 2, and Character 1584.v

• Label: 1584.2.v
• Level: $1584$
• Weight: $2$
• Character orbit: 1584.v
• Rep. character: $\chi_{1584}(683,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $160$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).

	Total	New	Old
Modular forms	592	160	432
Cusp forms	560	160	400
Eisenstein series	32	0	32

Trace form

\( 160 q + 16 q^{10} + 16 q^{16} - 32 q^{19} - 48 q^{34} - 144 q^{40} - 16 q^{46} + 160 q^{49} - 64 q^{58} + 64 q^{61} + 96 q^{70} + 64 q^{76} - 80 q^{82} + 64 q^{85} - 96 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)