Space of modular forms of level 2400, weight 2, and Character 2400.cm

• Label: 2400.2.cm
• Level: $2400$
• Weight: $2$
• Character orbit: 2400.cm
• Rep. character: $\chi_{2400}(431,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $464$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.cm (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 600 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2400, [\chi])\).

	Total	New	Old
Modular forms	1984	496	1488
Cusp forms	1856	464	1392
Eisenstein series	128	32	96

Trace form

\( 464 q + 6 q^{3} - 6 q^{9} + 12 q^{19} - 16 q^{25} + 6 q^{27} - 18 q^{33} - 400 q^{49} + 28 q^{51} - 4 q^{57} + 12 q^{67} - 12 q^{73} + 30 q^{75} - 6 q^{81} - 72 q^{91} - 36 q^{97} + 52 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)