Space of modular forms of level 500, weight 4, and Character 500.l

• Label: 500.4.l
• Level: $500$
• Weight: $4$
• Character orbit: 500.l
• Rep. character: $\chi_{500}(7,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1032$
• Sturm bound: $300$

Defining parameters

Level:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	500.l (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(300\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(500, [\chi])\).

	Total	New	Old
Modular forms	1880	1128	752
Cusp forms	1720	1032	688
Eisenstein series	160	96	64

Trace form

1032 * q + 8 * q^2 + 10 * q^4 - 18 * q^6 - 34 * q^8 + 20 * q^9 - 70 * q^12 + 62 * q^13 + 10 * q^14 - 18 * q^16 - 114 * q^17 + 316 * q^18 - 36 * q^21 + 370 * q^22 - 48 * q^26 - 870 * q^28 + 20 * q^29 - 622 * q^32 + 100 * q^33 + 10 * q^34 - 786 * q^36 + 346 * q^37 - 880 * q^38 - 36 * q^41 + 470 * q^42 + 1340 * q^44 - 18 * q^46 + 3400 * q^48 + 2356 * q^52 - 678 * q^53 + 3780 * q^54 - 18 * q^56 - 940 * q^57 + 1112 * q^58 - 36 * q^61 - 2900 * q^62 - 4820 * q^64 - 2610 * q^66 - 2418 * q^68 + 20 * q^69 - 1892 * q^72 + 1962 * q^73 + 720 * q^76 + 3140 * q^77 + 3460 * q^78 + 13086 * q^81 + 8826 * q^82 + 11290 * q^84 - 18 * q^86 + 1570 * q^88 - 1410 * q^89 - 6130 * q^92 + 1300 * q^93 - 11030 * q^94 - 5238 * q^96 + 12626 * q^97 - 13324 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(500, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(500, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(500, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)