Space of modular forms of level 360, weight 4, and Character 360.x

• Label: 360.4.x
• Level: $360$
• Weight: $4$
• Character orbit: 360.x
• Rep. character: $\chi_{360}(53,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(360, [\chi])\).

	Total	New	Old
Modular forms	448	144	304
Cusp forms	416	144	272
Eisenstein series	32	0	32

Trace form

\( 144 q + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)