Space of modular forms of level 1521, weight 4, and Character 1521.i

• Label: 1521.4.i
• Level: $1521$
• Weight: $4$
• Character orbit: 1521.i
• Rep. character: $\chi_{1521}(746,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $308$
• Sturm bound: $728$

Defining parameters

Level:	\( N \)	\(=\)	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1521.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1521, [\chi])\).

	Total	New	Old
Modular forms	1148	308	840
Cusp forms	1036	308	728
Eisenstein series	112	0	112

Trace form

\( 308 q + 64 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1521, [\chi]) \cong \)