Space of modular forms of level 550, weight 4, and Character 550.be

• Label: 550.4.be
• Level: $550$
• Weight: $4$
• Character orbit: 550.be
• Rep. character: $\chi_{550}(17,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $720$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	550.be (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(550, [\chi])\).

	Total	New	Old
Modular forms	2192	720	1472
Cusp forms	2128	720	1408
Eisenstein series	64	0	64

Trace form

720 * q + 8 * q^3 - 48 * q^5 + 100 * q^7 + 120 * q^10 - 32 * q^12 + 164 * q^15 + 2880 * q^16 - 640 * q^17 - 240 * q^19 - 64 * q^20 + 312 * q^22 + 176 * q^23 + 600 * q^25 - 364 * q^27 + 240 * q^28 - 832 * q^33 + 6480 * q^36 + 720 * q^37 + 72 * q^38 - 2800 * q^39 + 400 * q^42 + 496 * q^45 - 160 * q^47 - 128 * q^48 - 1380 * q^49 - 260 * q^53 + 2760 * q^54 + 1276 * q^55 - 560 * q^57 + 1344 * q^58 - 1280 * q^59 - 160 * q^60 - 80 * q^62 - 5520 * q^67 - 2560 * q^68 - 6860 * q^69 - 3456 * q^70 - 3720 * q^71 + 2940 * q^73 + 8644 * q^75 - 652 * q^77 - 5312 * q^78 - 1680 * q^79 - 512 * q^80 - 57040 * q^81 - 1200 * q^82 - 4700 * q^83 - 6840 * q^85 - 1632 * q^88 - 1264 * q^92 - 9092 * q^93 + 2240 * q^95 - 1536 * q^97 + 6560 * q^98 - 760 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(550, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(550, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(550, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)