Space of modular forms of level 320, weight 10, and Character 320.o

• Label: 320.10.o
• Level: $320$
• Weight: $10$
• Character orbit: 320.o
• Rep. character: $\chi_{320}(223,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $216$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	320.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(320, [\chi])\).

	Total	New	Old
Modular forms	888	216	672
Cusp forms	840	216	624
Eisenstein series	48	0	48

Trace form

\( 216 q + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)