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

• Label: 2499.4.bc
• Level: $2499$
• Weight: $4$
• Character orbit: 2499.bc
• Rep. character: $\chi_{2499}(361,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1440$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2499 = 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2499.bc (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	4096	1440	2656
Cusp forms	3968	1440	2528
Eisenstein series	128	0	128

Trace form

1440 * q + 2880 * q^4 + 16 * q^5 - 56 * q^11 - 416 * q^13 - 11520 * q^16 + 8 * q^17 + 352 * q^20 - 856 * q^22 - 112 * q^23 - 180 * q^24 - 112 * q^29 + 672 * q^30 - 176 * q^31 - 528 * q^33 - 1024 * q^34 + 600 * q^37 - 352 * q^38 + 288 * q^40 - 256 * q^41 - 336 * q^44 - 144 * q^45 + 1084 * q^46 - 368 * q^47 - 1056 * q^48 + 448 * q^50 - 840 * q^52 - 2304 * q^55 + 2784 * q^57 - 1660 * q^58 + 136 * q^61 + 2216 * q^62 - 89136 * q^64 - 2096 * q^65 - 1168 * q^67 + 832 * q^68 + 4416 * q^69 - 6112 * q^71 - 1104 * q^73 - 1548 * q^74 - 624 * q^75 + 4296 * q^78 - 2552 * q^79 - 808 * q^80 + 58320 * q^81 - 3028 * q^82 - 16416 * q^85 - 4536 * q^86 - 5332 * q^88 + 640 * q^89 - 2240 * q^92 + 1400 * q^95 + 1440 * q^96 + 144 * 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

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