Space of modular forms of level 1440, weight 4, and Character 1440.eh

• Label: 1440.4.eh
• Level: $1440$
• Weight: $4$
• Character orbit: 1440.eh
• Rep. character: $\chi_{1440}(43,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $6880$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1440.eh (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1440 \)
Character field:			\(\Q(\zeta_{24})\)
Sturm bound:			\(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1440, [\chi])\).

	Total	New	Old
Modular forms	6944	6944	0
Cusp forms	6880	6880	0
Eisenstein series	64	64	0

Trace form

6880 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 8 * q^12 - 4 * q^13 - 128 * q^14 - 16 * q^15 - 8 * q^16 - 40 * q^18 - 312 * q^20 - 16 * q^21 - 4 * q^22 - 736 * q^24 - 4 * q^25 - 32 * q^26 - 8 * q^27 - 528 * q^28 + 1684 * q^30 - 4 * q^32 - 16 * q^33 - 1016 * q^35 - 16 * q^36 - 16 * q^37 + 2404 * q^38 - 4 * q^40 - 8 * q^41 - 872 * q^42 - 4 * q^43 - 8 * q^45 - 32 * q^46 - 8 * q^47 - 2452 * q^48 + 163856 * q^49 + 60 * q^50 - 16 * q^51 - 4 * q^52 - 16 * q^53 + 5936 * q^54 - 16 * q^55 - 8 * q^56 - 16 * q^57 - 4 * q^58 - 264 * q^60 - 8 * q^61 - 80 * q^62 - 2744 * q^63 - 8 * q^65 + 6576 * q^66 - 4 * q^67 - 260 * q^68 - 216 * q^69 + 1368 * q^70 - 32 * q^71 - 2724 * q^72 - 32 * q^73 - 116 * q^75 - 2240 * q^76 - 2748 * q^77 + 5812 * q^78 - 16 * q^80 - 80 * q^82 - 4 * q^83 - 2744 * q^84 - 4 * q^85 - 8 * q^86 - 2592 * q^87 + 4172 * q^88 - 5976 * q^90 - 32 * q^91 - 6824 * q^92 - 116 * q^93 - 6192 * q^96 - 8 * q^97 - 2696 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

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