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

• Label: 539.4.w
• Level: $539$
• Weight: $4$
• Character orbit: 539.w
• Rep. character: $\chi_{539}(10,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1992$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	539.w (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 539 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(224\)

Dimensions

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

	Total	New	Old
Modular forms	2040	2040	0
Cusp forms	1992	1992	0
Eisenstein series	48	48	0

Trace form

1992 * q - 22 * q^3 - 682 * q^4 + 2 * q^5 - 1484 * q^9 + 85 * q^11 + 26 * q^12 + 128 * q^14 - 332 * q^15 + 2546 * q^16 - 924 * q^20 + 230 * q^22 - 754 * q^23 - 3612 * q^25 + 394 * q^26 - 112 * q^27 - 864 * q^31 + 787 * q^33 - 1344 * q^34 - 10780 * q^36 + 58 * q^37 - 3508 * q^38 + 5832 * q^42 - 2942 * q^44 - 5396 * q^45 + 1638 * q^47 + 5104 * q^49 - 4310 * q^53 + 1876 * q^55 - 4140 * q^56 + 3150 * q^58 - 4326 * q^59 - 4364 * q^60 + 23636 * q^64 + 720 * q^66 + 520 * q^67 + 10892 * q^69 + 1602 * q^70 + 540 * q^71 - 6580 * q^75 + 201 * q^77 + 3318 * q^78 - 7812 * q^80 + 29374 * q^81 + 5186 * q^82 + 924 * q^86 - 2083 * q^88 - 1102 * q^89 - 17572 * q^91 + 4474 * q^92 + 1384 * q^93 + 9520 * 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.