Space of modular forms of level 1584, weight 4, and Character 1584.dq

• Label: 1584.4.dq
• Level: $1584$
• Weight: $4$
• Character orbit: 1584.dq
• Rep. character: $\chi_{1584}(59,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $13760$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1584.dq (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1584 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1584, [\chi])\).

	Total	New	Old
Modular forms	13888	13888	0
Cusp forms	13760	13760	0
Eisenstein series	128	128	0

Trace form

13760 * q - 18 * q^2 - 12 * q^3 - 6 * q^4 - 18 * q^5 - 12 * q^6 - 12 * q^7 - 64 * q^10 - 24 * q^11 - 32 * q^12 - 6 * q^13 - 18 * q^14 - 6 * q^16 - 44 * q^18 - 24 * q^19 - 18 * q^20 - 140 * q^21 - 8 * q^22 - 96 * q^23 - 748 * q^24 - 12 * q^27 - 536 * q^28 - 18 * q^29 - 44 * q^30 - 48 * q^32 - 32 * q^33 - 48 * q^34 + 244 * q^36 - 24 * q^37 - 18 * q^38 - 24 * q^39 - 6 * q^40 - 536 * q^42 - 16 * q^43 - 532 * q^45 - 120 * q^46 - 32 * q^48 + 81916 * q^49 - 18 * q^50 - 228 * q^51 - 6 * q^52 - 5748 * q^54 - 64 * q^55 - 4164 * q^56 - 6 * q^58 - 18 * q^59 - 2696 * q^60 - 6 * q^61 - 24 * q^64 - 96 * q^65 - 836 * q^66 - 16 * q^67 - 14592 * q^68 - 174 * q^69 - 2064 * q^70 + 6154 * q^72 - 18 * q^74 - 404 * q^75 - 16 * q^76 - 24 * q^77 + 3016 * q^78 - 24 * q^81 - 88 * q^82 - 18 * q^83 - 7506 * q^84 - 506 * q^85 - 18 * q^86 - 64 * q^87 - 8360 * q^88 + 10596 * q^90 - 2768 * q^91 + 18906 * q^92 + 96 * q^93 - 70 * q^94 + 6164 * q^96 - 12 * q^97 + 1182 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

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