Space of modular forms of level 2496, weight 4, and Character 2496.fn

• Label: 2496.4.fn
• Level: $2496$
• Weight: $4$
• Character orbit: 2496.fn
• Rep. character: $\chi_{2496}(35,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $21440$
• Sturm bound: $1792$

Defining parameters

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2496.fn (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2496 \)
Character field:			\(\Q(\zeta_{48})\)
Sturm bound:			\(1792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2496, [\chi])\).

	Total	New	Old
Modular forms	21568	21568	0
Cusp forms	21440	21440	0
Eisenstein series	128	128	0

Trace form

21440 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 32 * q^12 - 32 * q^13 - 8 * q^15 - 16 * q^16 - 32 * q^18 - 16 * q^19 - 32 * q^21 - 16 * q^22 - 8 * q^24 - 64 * q^25 - 32 * q^27 - 16 * q^28 - 8 * q^30 - 128 * q^31 - 64 * q^34 - 8 * q^36 - 16 * q^37 - 16 * q^39 - 64 * q^40 - 8 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 32 * q^51 - 3344 * q^52 - 8 * q^54 + 560 * q^55 - 32 * q^57 + 9488 * q^58 - 32 * q^60 - 16 * q^61 - 64 * q^64 + 96 * q^66 - 16 * q^67 - 8 * q^69 - 8128 * q^70 - 8 * q^72 - 64 * q^73 - 8 * q^75 - 16 * q^76 - 5080 * q^78 - 64 * q^79 - 8 * q^81 - 13936 * q^82 - 8 * q^84 - 16 * q^85 - 8 * q^87 - 3136 * q^88 + 18688 * q^90 - 32 * q^91 - 224 * q^93 - 16 * q^94 - 32 * q^96 - 32 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(2496, [\chi])\) into newform subspaces

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