Space of modular forms of level 1575, weight 4, and Character 1575.g

• Label: 1575.4.g
• Level: $1575$
• Weight: $4$
• Character orbit: 1575.g
• Rep. character: $\chi_{1575}(1574,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1575.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1575, [\chi])\).

	Total	New	Old
Modular forms	744	144	600
Cusp forms	696	144	552
Eisenstein series	48	0	48

Trace form

\( 144 q + 576 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)