Space of modular forms of level 3724, weight 2, and Character 3724.w

• Label: 3724.2.w
• Level: $3724$
• Weight: $2$
• Character orbit: 3724.w
• Rep. character: $\chi_{3724}(2775,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $720$
• Sturm bound: $1120$

Defining parameters

Level:	\( N \)	\(=\)	\( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3724.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3724, [\chi])\).

	Total	New	Old
Modular forms	1152	720	432
Cusp forms	1088	720	368
Eisenstein series	64	0	64

Trace form

720 * q - 4 * q^2 + 4 * q^4 + 8 * q^8 - 360 * q^9 + 30 * q^12 + 28 * q^16 - 10 * q^18 - 8 * q^22 - 36 * q^24 + 368 * q^25 + 80 * q^29 - 56 * q^30 + 46 * q^32 + 24 * q^33 + 40 * q^36 - 32 * q^37 + 60 * q^40 + 16 * q^44 - 24 * q^45 + 12 * q^46 + 60 * q^50 - 18 * q^52 + 32 * q^53 - 54 * q^54 + 40 * q^58 - 48 * q^60 - 32 * q^64 + 36 * q^68 - 60 * q^72 + 26 * q^74 + 52 * q^78 - 60 * q^80 - 320 * q^81 - 12 * q^82 + 24 * q^85 + 128 * q^86 - 74 * q^88 + 120 * q^89 - 112 * q^92 + 16 * q^93 + 18 * q^94 - 144 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(3724, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3724, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3724, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)