Space of modular forms of level 538, weight 4, and Character 538.e

• Label: 538.4.e
• Level: $538$
• Weight: $4$
• Character orbit: 538.e
• Rep. character: $\chi_{538}(9,\cdot)$
• Character field: $\Q(\zeta_{134})$
• Dimension: $4488$
• Sturm bound: $270$

Defining parameters

Level:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	538.e (of order \(134\) and degree \(66\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 269 \)
Character field:			\(\Q(\zeta_{134})\)
Sturm bound:			\(270\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(538, [\chi])\).

	Total	New	Old
Modular forms	13464	4488	8976
Cusp forms	13200	4488	8712
Eisenstein series	264	0	264

Trace form

4488 * q + 272 * q^4 - 38 * q^5 + 4 * q^6 + 594 * q^9 - 18 * q^11 + 114 * q^13 - 8 * q^14 - 1088 * q^16 + 152 * q^20 + 20 * q^21 + 224 * q^23 - 16 * q^24 - 1098 * q^25 - 384 * q^30 + 600 * q^34 - 2376 * q^36 - 4522 * q^37 - 436 * q^38 + 624 * q^41 + 654 * q^43 + 72 * q^44 + 1074 * q^45 + 3730 * q^47 + 3052 * q^49 - 596 * q^51 - 456 * q^52 - 326 * q^53 - 1504 * q^54 - 828 * q^55 + 32 * q^56 + 1024 * q^57 + 100 * q^58 + 11792 * q^60 - 226 * q^61 - 312 * q^62 + 4352 * q^64 - 316 * q^65 - 2480 * q^66 + 1318 * q^67 - 608 * q^70 - 14454 * q^73 + 1152 * q^78 + 1444 * q^79 - 608 * q^80 - 3204 * q^81 + 32964 * q^83 - 80 * q^84 + 5600 * q^87 + 1284 * q^89 - 896 * q^92 - 11140 * q^93 + 64 * q^96 + 288 * q^97 - 3370 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(538, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(538, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(538, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(269, [\chi])\)\(^{\oplus 2}\)