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

• Label: 1440.4.ce
• Level: $1440$
• Weight: $4$
• Character orbit: 1440.ce
• Rep. character: $\chi_{1440}(307,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $1432$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1440.ce (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 160 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(1152\)

Dimensions

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

	Total	New	Old
Modular forms	3488	1448	2040
Cusp forms	3424	1432	1992
Eisenstein series	64	16	48

Trace form

1432 * q + 4 * q^2 + 4 * q^5 + 88 * q^8 + 8 * q^10 + 8 * q^11 - 4 * q^13 - 64 * q^14 - 8 * q^16 + 48 * q^19 + 312 * q^20 + 428 * q^22 - 4 * q^25 + 8 * q^26 + 252 * q^28 - 336 * q^32 - 696 * q^34 - 40 * q^35 - 4 * q^37 + 2244 * q^38 + 816 * q^40 + 8 * q^41 - 868 * q^43 + 1232 * q^44 - 8 * q^46 + 8 * q^47 - 67816 * q^49 + 36 * q^50 + 3416 * q^52 + 4 * q^53 + 284 * q^55 - 328 * q^56 + 2012 * q^58 - 1832 * q^61 - 496 * q^62 + 816 * q^64 + 8 * q^65 + 1844 * q^67 + 1744 * q^68 + 1764 * q^70 - 216 * q^71 - 8 * q^73 - 664 * q^76 - 1368 * q^77 - 1792 * q^80 - 6372 * q^82 + 2684 * q^83 - 4 * q^85 - 1176 * q^86 - 3096 * q^88 - 8 * q^91 + 8828 * q^92 + 416 * q^94 - 8 * q^97 + 808 * 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.

Decomposition of \(S_{4}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1440, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)