Space of modular forms of level 539, weight 4, and Character 539.s

• Label: 539.4.s
• Level: $539$
• Weight: $4$
• Character orbit: 539.s
• Rep. character: $\chi_{539}(19,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $928$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	539.s (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(539, [\chi])\).

	Total	New	Old
Modular forms	1408	992	416
Cusp forms	1280	928	352
Eisenstein series	128	64	64

Trace form

928 * q + 5 * q^2 + 9 * q^3 - 425 * q^4 - 15 * q^5 + 120 * q^8 - 1065 * q^9 + 32 * q^11 - 24 * q^12 - 120 * q^15 + 1595 * q^16 + 45 * q^17 + 455 * q^18 + 15 * q^19 - 1408 * q^22 - 180 * q^23 + 1365 * q^24 - 2645 * q^25 + 57 * q^26 + 660 * q^29 + 545 * q^30 - 1233 * q^31 + 1614 * q^33 - 3402 * q^36 + 375 * q^37 + 135 * q^38 - 1835 * q^39 - 2145 * q^40 + 1447 * q^44 - 2610 * q^45 - 2425 * q^46 - 447 * q^47 - 1290 * q^50 - 195 * q^51 + 15 * q^52 + 851 * q^53 - 600 * q^57 - 995 * q^58 + 477 * q^59 - 341 * q^60 + 2475 * q^61 + 13072 * q^64 + 1695 * q^66 + 5104 * q^67 - 465 * q^68 + 632 * q^71 + 3215 * q^72 - 2865 * q^73 - 1885 * q^74 - 2313 * q^75 - 10996 * q^78 - 2545 * q^79 - 9495 * q^80 + 233 * q^81 - 7959 * q^82 + 23280 * q^85 + 9173 * q^86 + 847 * q^88 - 1536 * q^89 - 1120 * q^92 - 6033 * q^93 + 18615 * q^94 + 8215 * q^95 - 7635 * q^96 - 18136 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(539, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(539, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(539, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)