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

• Label: 2940.2.cm
• Level: $2940$
• Weight: $2$
• Character orbit: 2940.cm
• Rep. character: $\chi_{2940}(121,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $456$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.cm (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	8208	456	7752
Cusp forms	7920	456	7464
Eisenstein series	288	0	288

Trace form

456 * q + 2 * q^3 + 2 * q^7 + 38 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^17 - 6 * q^19 - 4 * q^21 + 38 * q^25 - 4 * q^27 + 8 * q^29 + 2 * q^31 + 8 * q^33 - 28 * q^35 - 4 * q^37 + 4 * q^39 - 32 * q^41 + 20 * q^43 - 104 * q^47 - 74 * q^49 - 52 * q^51 - 112 * q^53 - 8 * q^55 + 20 * q^57 - 88 * q^59 - 26 * q^61 - 12 * q^63 - 4 * q^65 - 2 * q^67 + 8 * q^69 - 32 * q^71 + 110 * q^73 + 2 * q^75 + 120 * q^77 + 6 * q^79 + 38 * q^81 + 140 * q^83 - 8 * q^85 + 292 * q^89 + 174 * q^91 - 2 * q^93 + 8 * q^95 + 160 * q^97 + 8 * q^99

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)