Space of modular forms of level 1575, weight 2, and Character 1575.bz

• Label: 1575.2.bz
• Level: $1575$
• Weight: $2$
• Character orbit: 1575.bz
• Rep. character: $\chi_{1575}(566,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $320$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.bz (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 525 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

	Total	New	Old
Modular forms	992	320	672
Cusp forms	928	320	608
Eisenstein series	64	0	64

Trace form

\( 320 q + 80 q^{4} - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

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