Space of modular forms of level 3520, weight 2, and Character 3520.fd

• Label: 3520.2.fd
• Level: $3520$
• Weight: $2$
• Character orbit: 3520.fd
• Rep. character: $\chi_{3520}(51,\cdot)$
• Character field: $\Q(\zeta_{80})$
• Dimension: $12288$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3520.fd (of order \(80\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 704 \)
Character field:			\(\Q(\zeta_{80})\)
Sturm bound:			\(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3520, [\chi])\).

	Total	New	Old
Modular forms	18560	12288	6272
Cusp forms	18304	12288	6016
Eisenstein series	256	0	256

Trace form

\( 12288 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 2}\)