Space of modular forms of level 576, weight 8, and Character 576.bm

• Label: 576.8.bm
• Level: $576$
• Weight: $8$
• Character orbit: 576.bm
• Rep. character: $\chi_{576}(13,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $10720$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	576.bm (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 576 \)
Character field:			\(\Q(\zeta_{48})\)
Sturm bound:			\(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(576, [\chi])\).

	Total	New	Old
Modular forms	10784	10784	0
Cusp forms	10720	10720	0
Eisenstein series	64	64	0

Trace form

10720 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 - 1196096 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 + 1739904 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 4069536 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 - 7717856 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 10358144 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 2080 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 1040 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 - 29207192 * q^76 - 8 * q^77 - 39347608 * q^78 - 8 * q^79 + 93615968 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 17056832 * q^84 - 8 * q^85 - 139071096 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 31734016 * q^90 - 32 * q^91 - 54440784 * q^92 - 17512 * q^93 - 8 * q^94 + 112868968 * q^96 + 125538032 * q^98 - 16 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

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