Space of modular forms of level 2499, weight 4, and Character 2499.v

• Label: 2499.4.v
• Level: $2499$
• Weight: $4$
• Character orbit: 2499.v
• Rep. character: $\chi_{2499}(1324,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $1480$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2499 = 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2499.v (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2499, [\chi])\).

	Total	New	Old
Modular forms	4096	1480	2616
Cusp forms	3968	1480	2488
Eisenstein series	128	0	128

Trace form

1480 * q - 32 * q^5 - 24 * q^6 + 128 * q^10 - 112 * q^11 - 24064 * q^16 - 144 * q^17 - 32 * q^19 - 640 * q^20 - 728 * q^22 + 208 * q^23 + 456 * q^24 - 600 * q^25 - 1272 * q^29 - 192 * q^31 - 1520 * q^32 + 144 * q^33 + 24 * q^34 - 216 * q^36 + 416 * q^37 - 48 * q^39 + 2408 * q^40 - 1064 * q^41 - 576 * q^43 - 1184 * q^44 + 504 * q^45 + 2304 * q^46 + 448 * q^50 - 4032 * q^52 + 5672 * q^53 - 216 * q^54 + 768 * q^57 + 2152 * q^58 + 1152 * q^59 - 1320 * q^60 + 4816 * q^61 - 288 * q^62 - 6472 * q^65 - 1248 * q^66 - 1824 * q^67 + 15312 * q^68 - 960 * q^69 - 3776 * q^71 - 2184 * q^73 - 208 * q^74 + 96 * q^75 - 824 * q^76 + 4872 * q^78 + 512 * q^79 + 8656 * q^80 - 10888 * q^82 - 8896 * q^83 + 3096 * q^85 + 10368 * q^86 + 1872 * q^87 + 5432 * q^88 - 1152 * q^90 + 5424 * q^92 - 2928 * q^93 - 6064 * q^94 - 4528 * q^95 - 1344 * q^96 - 1296 * q^97 - 1008 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(2499, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2499, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2499, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)