Space of modular forms of level 1200, weight 2, and Character 1200.by

• Label: 1200.2.by
• Level: $1200$
• Weight: $2$
• Character orbit: 1200.by
• Rep. character: $\chi_{1200}(239,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $240$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1200.by (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 300 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

	Total	New	Old
Modular forms	1008	240	768
Cusp forms	912	240	672
Eisenstein series	96	0	96

Trace form

\( 240 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)