Space of modular forms of level 3744, weight 2, and Character 3744.jo

• Label: 3744.2.jo
• Level: $3744$
• Weight: $2$
• Character orbit: 3744.jo
• Rep. character: $\chi_{3744}(829,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $2224$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3744.jo (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 416 \)
Character field:			\(\Q(\zeta_{24})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).

	Total	New	Old
Modular forms	5440	2256	3184
Cusp forms	5312	2224	3088
Eisenstein series	128	32	96

Trace form

2224 * q + 12 * q^2 - 4 * q^4 - 12 * q^7 - 4 * q^10 + 12 * q^11 - 8 * q^13 - 16 * q^14 - 4 * q^16 - 12 * q^19 + 60 * q^20 + 12 * q^22 + 4 * q^23 - 16 * q^25 + 48 * q^26 - 72 * q^28 + 4 * q^29 + 72 * q^32 + 4 * q^35 - 12 * q^37 + 56 * q^38 - 56 * q^40 + 12 * q^41 - 4 * q^43 - 12 * q^46 + 12 * q^50 + 80 * q^52 + 16 * q^53 - 36 * q^55 - 36 * q^56 - 12 * q^58 + 108 * q^59 - 4 * q^61 - 40 * q^62 - 16 * q^64 + 16 * q^65 - 12 * q^67 + 60 * q^68 + 12 * q^71 + 4 * q^74 - 12 * q^76 + 16 * q^77 + 12 * q^80 - 84 * q^82 - 72 * q^85 - 44 * q^88 + 12 * q^89 + 40 * q^91 - 128 * q^92 - 36 * q^94 + 136 * q^95 - 24 * q^97 + 12 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)