Space of modular forms of level 588, weight 4, and Character 588.o

• Label: 588.4.o
• Level: $588$
• Weight: $4$
• Character orbit: 588.o
• Rep. character: $\chi_{588}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $240$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(588, [\chi])\).

	Total	New	Old
Modular forms	704	240	464
Cusp forms	640	240	400
Eisenstein series	64	0	64

Trace form

240 * q + 4 * q^2 + 20 * q^4 + 220 * q^8 - 1080 * q^9 - 18 * q^10 - 116 * q^16 + 36 * q^18 + 196 * q^22 + 270 * q^24 + 2916 * q^25 + 750 * q^26 - 1600 * q^29 + 168 * q^30 - 286 * q^32 + 36 * q^33 - 360 * q^36 + 284 * q^37 - 1494 * q^38 - 1170 * q^40 - 2320 * q^44 + 776 * q^46 - 1792 * q^50 + 3564 * q^52 + 1896 * q^53 + 504 * q^57 + 3670 * q^58 - 1014 * q^60 + 600 * q^61 + 1880 * q^64 - 280 * q^65 - 2052 * q^66 - 7452 * q^68 - 990 * q^72 + 972 * q^73 + 1098 * q^74 - 1620 * q^78 + 5976 * q^80 - 9720 * q^81 + 9816 * q^82 - 4944 * q^85 + 18 * q^86 + 3114 * q^88 + 10864 * q^92 - 12 * q^93 - 9072 * q^94 - 3870 * q^96

Decomposition of \(S_{4}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(588, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)