Space of modular forms of level 600, weight 8, and Character 600.bq

• Label: 600.8.bq
• Level: $600$
• Weight: $8$
• Character orbit: 600.bq
• Rep. character: $\chi_{600}(67,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $3360$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	600.bq (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(600, [\chi])\).

	Total	New	Old
Modular forms	6752	3360	3392
Cusp forms	6688	3360	3328
Eisenstein series	64	0	64

Trace form

3360 * q - 2004 * q^8 + 3592 * q^10 + 15336 * q^12 - 5816 * q^17 - 113980 * q^20 + 27636 * q^22 + 32248 * q^25 - 58132 * q^28 + 338472 * q^30 - 35540 * q^32 + 1633008 * q^35 + 494780 * q^38 + 6937012 * q^40 - 97740 * q^42 + 1505696 * q^43 - 11667740 * q^44 + 544752 * q^48 - 11902076 * q^50 + 5086476 * q^52 - 163224 * q^58 - 1934820 * q^60 - 19863748 * q^62 - 27484860 * q^64 - 2093512 * q^65 + 18376464 * q^67 + 17215224 * q^68 - 16380844 * q^70 + 1460916 * q^72 + 13426520 * q^73 + 10918152 * q^78 + 17175764 * q^80 + 446410440 * q^81 - 42267488 * q^82 + 1006960 * q^83 + 75118320 * q^84 - 62997476 * q^88 + 119526200 * q^89 - 37756368 * q^90 - 89714712 * q^92 - 8667640 * q^94 - 8504460 * q^96 + 48269688 * q^97 + 189099264 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)