Space of modular forms of level 2352, weight 4, and Character 2352.w

• Label: 2352.4.w
• Level: $2352$
• Weight: $4$
• Character orbit: 2352.w
• Rep. character: $\chi_{2352}(589,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $984$
• Sturm bound: $1792$

Defining parameters

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2352.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(1792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2352, [\chi])\).

	Total	New	Old
Modular forms	2720	984	1736
Cusp forms	2656	984	1672
Eisenstein series	64	0	64

Trace form

984 * q + 20 * q^4 - 84 * q^8 + 48 * q^10 + 40 * q^11 - 24 * q^12 + 120 * q^15 - 72 * q^16 + 36 * q^18 + 24 * q^19 - 80 * q^20 - 272 * q^22 + 228 * q^24 - 20 * q^26 - 400 * q^29 - 408 * q^30 + 744 * q^31 - 960 * q^32 - 992 * q^34 + 108 * q^36 - 16 * q^37 + 816 * q^38 - 104 * q^40 - 376 * q^43 + 1264 * q^44 - 32 * q^46 + 528 * q^48 - 3548 * q^50 + 744 * q^51 - 3744 * q^52 - 752 * q^53 + 108 * q^54 - 1936 * q^58 + 1376 * q^59 + 1224 * q^60 - 912 * q^61 - 1932 * q^62 + 56 * q^64 + 976 * q^65 + 1368 * q^66 + 2256 * q^67 + 2472 * q^68 - 528 * q^69 + 612 * q^72 - 1060 * q^74 + 1104 * q^75 - 3104 * q^76 - 1692 * q^78 + 5992 * q^79 - 7032 * q^80 - 79704 * q^81 - 3520 * q^82 + 2680 * q^83 - 240 * q^85 + 13624 * q^86 - 1712 * q^88 + 648 * q^90 + 4568 * q^92 - 1568 * q^94 + 7728 * q^95 - 2280 * q^96 + 360 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2352, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)