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

• Label: 539.4.m
• Level: $539$
• Weight: $4$
• Character orbit: 539.m
• Rep. character: $\chi_{539}(195,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $464$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	539.m (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(224\)

Dimensions

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

	Total	New	Old
Modular forms	704	496	208
Cusp forms	640	464	176
Eisenstein series	64	32	32

Trace form

464 * q + 10 * q^2 + 434 * q^4 + 60 * q^8 + 1074 * q^9 - 20 * q^11 - 276 * q^15 - 1622 * q^16 - 440 * q^18 + 664 * q^22 + 624 * q^23 + 1562 * q^25 - 720 * q^29 - 530 * q^30 - 1230 * q^36 - 618 * q^37 + 1850 * q^39 - 3448 * q^44 + 2440 * q^46 + 1230 * q^50 + 2730 * q^51 - 1682 * q^53 + 540 * q^57 + 3572 * q^58 + 3458 * q^60 + 3728 * q^64 + 1304 * q^67 - 3632 * q^71 - 16520 * q^72 - 3770 * q^74 + 1012 * q^78 - 590 * q^79 - 10394 * q^81 + 5340 * q^85 - 10916 * q^86 + 12626 * q^88 + 442 * q^92 + 9822 * q^93 - 4210 * q^95 + 544 * 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

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