Space of modular forms of level 1110, weight 4, and Character 1110.by

• Label: 1110.4.by
• Level: $1110$
• Weight: $4$
• Character orbit: 1110.by
• Rep. character: $\chi_{1110}(59,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $2736$
• Sturm bound: $912$

Defining parameters

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1110.by (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 555 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1110, [\chi])\).

	Total	New	Old
Modular forms	8304	2736	5568
Cusp forms	8112	2736	5376
Eisenstein series	192	0	192

Trace form

\( 2736 q + 384 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)