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

• Label: 2940.2.n
• Level: $2940$
• Weight: $2$
• Character orbit: 2940.n
• Rep. character: $\chi_{2940}(491,\cdot)$
• Character field: $\Q$
• Dimension: $328$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	704	328	376
Cusp forms	640	328	312
Eisenstein series	64	0	64

Trace form

328 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^10 - 16 * q^12 + 8 * q^13 + 18 * q^16 - 4 * q^18 + 4 * q^22 + 18 * q^24 - 328 * q^25 + 8 * q^30 - 16 * q^33 + 28 * q^34 - 22 * q^36 - 8 * q^37 + 14 * q^40 + 4 * q^45 - 12 * q^46 + 48 * q^48 - 8 * q^52 - 6 * q^54 + 24 * q^57 - 68 * q^58 + 14 * q^60 - 24 * q^61 + 46 * q^64 - 28 * q^66 - 12 * q^69 - 76 * q^72 + 48 * q^73 - 60 * q^76 + 24 * q^78 + 40 * q^81 - 8 * q^82 + 16 * q^85 - 36 * q^88 - 18 * q^90 + 64 * q^93 + 60 * q^94 - 18 * q^96

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)