Space of modular forms of level 2940, weight 2, and Character 2940.cw

• Label: 2940.2.cw
• Level: $2940$
• Weight: $2$
• Character orbit: 2940.cw
• Rep. character: $\chi_{2940}(89,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1344$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.cw (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 735 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2940, [\chi])\).

	Total	New	Old
Modular forms	8208	1344	6864
Cusp forms	7920	1344	6576
Eisenstein series	288	0	288

Trace form

\( 1344 q - 16 q^{9} + 6 q^{15} - 12 q^{19} + 8 q^{21} - 2 q^{25} + 12 q^{31} - 10 q^{39} - 12 q^{45} - 12 q^{49} + 12 q^{51} - 14 q^{55} + 80 q^{61} - 21 q^{75} + 40 q^{79} - 68 q^{85} - 128 q^{91} + 96 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2940, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2940, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)