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

• Label: 2499.4.cm
• Level: $2499$
• Weight: $4$
• Character orbit: 2499.cm
• Rep. character: $\chi_{2499}(4,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $12096$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2499 = 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2499.cm (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 833 \)
Character field:			\(\Q(\zeta_{84})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	24288	12096	12192
Cusp forms	24096	12096	12000
Eisenstein series	192	0	192

Trace form

12096 * q - 4032 * q^4 + 16 * q^5 - 8 * q^7 - 448 * q^11 - 416 * q^13 + 336 * q^14 + 16128 * q^16 + 8 * q^17 - 1440 * q^20 - 280 * q^22 - 112 * q^23 - 1440 * q^24 - 524 * q^28 - 112 * q^29 + 672 * q^30 - 176 * q^31 - 528 * q^33 + 4240 * q^34 - 1184 * q^35 + 168 * q^37 - 352 * q^38 - 720 * q^40 + 640 * q^41 - 8960 * q^44 + 1872 * q^45 + 700 * q^46 + 4784 * q^47 - 1056 * q^48 + 448 * q^50 - 840 * q^52 - 2304 * q^55 + 10620 * q^56 + 4004 * q^58 + 136 * q^61 - 12792 * q^62 - 72 * q^63 + 132048 * q^64 - 112 * q^67 + 832 * q^68 + 4416 * q^69 + 2688 * q^71 - 1104 * q^73 - 2156 * q^74 - 624 * q^75 + 6888 * q^78 - 1176 * q^79 - 808 * q^80 - 81648 * q^81 + 37012 * q^82 - 72 * q^84 - 5264 * q^85 - 31976 * q^86 + 3220 * q^88 + 640 * q^89 - 11624 * q^91 - 2240 * q^92 - 40040 * q^95 + 11520 * q^96 + 144 * q^97 + 55016 * q^98 + 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

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