Space of modular forms of level 1200, weight 4, and Character 1200.t

• Label: 1200.4.t
• Level: $1200$
• Weight: $4$
• Character orbit: 1200.t
• Rep. character: $\chi_{1200}(299,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $856$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1200.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 240 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

	Total	New	Old
Modular forms	1464	872	592
Cusp forms	1416	856	560
Eisenstein series	48	16	32

Trace form

\( 856 q + 8 q^{4} - 4 q^{6} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \cong \)