Space of modular forms of level 1600, weight 4, and Character 1600.cs

• Label: 1600.4.cs
• Level: $1600$
• Weight: $4$
• Character orbit: 1600.cs
• Rep. character: $\chi_{1600}(67,\cdot)$
• Character field: $\Q(\zeta_{80})$
• Dimension: $22976$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1600.cs (of order \(80\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1600 \)
Character field:			\(\Q(\zeta_{80})\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1600, [\chi])\).

	Total	New	Old
Modular forms	23104	23104	0
Cusp forms	22976	22976	0
Eisenstein series	128	128	0

Trace form

22976 * q - 32 * q^2 - 32 * q^3 - 40 * q^4 - 32 * q^5 - 24 * q^6 - 32 * q^7 - 32 * q^8 - 40 * q^9 - 32 * q^10 - 24 * q^11 + 64 * q^12 - 32 * q^13 - 40 * q^14 - 32 * q^15 - 24 * q^16 - 40 * q^17 - 32 * q^18 - 40 * q^19 - 32 * q^20 - 24 * q^21 + 832 * q^22 - 32 * q^23 - 32 * q^25 - 64 * q^26 - 32 * q^27 - 32 * q^28 - 40 * q^29 - 2416 * q^30 - 48 * q^31 - 32 * q^32 - 168 * q^34 - 32 * q^35 - 24 * q^36 - 32 * q^37 - 9664 * q^38 - 40 * q^39 - 6016 * q^40 - 24 * q^41 - 32 * q^42 - 32 * q^43 - 40 * q^44 + 184 * q^45 - 24 * q^46 - 24 * q^47 + 4856 * q^48 + 4232 * q^50 - 64 * q^51 - 32 * q^52 - 32 * q^53 - 40 * q^54 - 32 * q^55 - 24 * q^56 - 32 * q^57 + 4000 * q^58 - 40 * q^59 - 24448 * q^60 - 24 * q^61 + 32 * q^62 - 40 * q^64 - 64 * q^65 - 24 * q^66 - 32 * q^67 - 3512 * q^68 - 40 * q^69 - 32 * q^70 - 24 * q^71 - 2792 * q^72 - 32 * q^73 - 32 * q^75 - 64 * q^76 - 32 * q^77 - 11736 * q^78 - 40 * q^79 - 32 * q^80 - 24 * q^81 + 12768 * q^82 - 32 * q^83 - 40 * q^84 - 1032 * q^85 - 24 * q^86 - 2608 * q^87 - 2496 * q^88 - 40 * q^89 - 32 * q^90 - 24 * q^91 - 34824 * q^92 + 184 * q^93 + 88 * q^94 - 64 * q^95 + 51576 * q^96 + 6344 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

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