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

• Label: 539.4.v
• Level: $539$
• Weight: $4$
• Character orbit: 539.v
• Rep. character: $\chi_{539}(15,\cdot)$
• Character field: $\Q(\zeta_{35})$
• Dimension: $3984$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	539.v (of order \(35\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 539 \)
Character field:			\(\Q(\zeta_{35})\)
Sturm bound:			\(224\)

Dimensions

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

	Total	New	Old
Modular forms	4080	4080	0
Cusp forms	3984	3984	0
Eisenstein series	96	96	0

Trace form

3984 * q - 15 * q^2 - 15 * q^3 + 641 * q^4 + q^5 - 23 * q^6 - 47 * q^8 + 1443 * q^9 - 280 * q^10 + 78 * q^11 - 180 * q^12 + 37 * q^13 + 70 * q^14 - 753 * q^15 + 2569 * q^16 - 371 * q^17 + 48 * q^18 - 1084 * q^19 - 903 * q^20 + 58 * q^21 - 680 * q^22 - 348 * q^23 + 1307 * q^24 + 4215 * q^25 + 769 * q^26 - 33 * q^27 - 658 * q^28 + 405 * q^29 - 406 * q^30 + 792 * q^31 - 328 * q^32 - 1734 * q^33 - 5152 * q^34 + 1282 * q^35 + 6287 * q^36 + 489 * q^37 + 1885 * q^38 + 157 * q^39 - 1843 * q^40 + 221 * q^41 - 4615 * q^42 + 800 * q^43 + 1558 * q^44 - 4568 * q^45 - 751 * q^46 - 1053 * q^47 - 2194 * q^48 - 3888 * q^49 + 1130 * q^50 + 1557 * q^51 - 1335 * q^52 + 4465 * q^53 - 934 * q^54 + 454 * q^55 - 4362 * q^56 + 1711 * q^57 + 5833 * q^58 + 4453 * q^59 + 14137 * q^60 + 2013 * q^61 - 2407 * q^62 - 583 * q^63 + 1329 * q^64 + 2484 * q^65 + 1592 * q^66 - 3904 * q^67 - 4160 * q^68 - 9045 * q^69 - 6933 * q^70 - 1135 * q^71 - 6455 * q^72 + 6917 * q^73 + 4657 * q^74 - 5431 * q^75 - 5848 * q^76 + 1259 * q^77 - 22324 * q^78 - 2640 * q^79 - 3958 * q^80 - 1161 * q^81 + 2113 * q^82 - 3143 * q^83 + 9457 * q^84 + 3965 * q^85 - 4636 * q^86 + 4624 * q^87 - 6228 * q^88 + 3272 * q^89 + 10223 * q^90 + 7320 * q^91 + 2668 * q^92 + 4791 * q^93 + 18041 * q^94 - 4001 * q^95 + 3799 * q^96 - 4908 * q^97 - 5722 * q^98 + 36212 * 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.