Space of modular forms of level 1600, weight 2, and Character 1600.br

• Label: 1600.2.br
• Level: $1600$
• Weight: $2$
• Character orbit: 1600.br
• Rep. character: $\chi_{1600}(107,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $1136$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.br (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 320 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).

	Total	New	Old
Modular forms	1968	1168	800
Cusp forms	1872	1136	736
Eisenstein series	96	32	64

Trace form

1136 * q + 8 * q^2 + 8 * q^3 - 16 * q^6 + 8 * q^7 + 8 * q^8 - 16 * q^11 + 40 * q^12 + 8 * q^13 + 64 * q^14 - 16 * q^16 + 16 * q^17 + 8 * q^18 - 16 * q^21 - 24 * q^22 + 8 * q^23 - 32 * q^24 - 16 * q^26 + 8 * q^27 + 8 * q^28 - 32 * q^31 + 8 * q^32 - 32 * q^34 - 16 * q^36 + 8 * q^37 - 48 * q^38 - 16 * q^41 + 8 * q^42 + 8 * q^43 - 16 * q^46 + 112 * q^48 + 48 * q^51 + 8 * q^52 + 8 * q^53 + 32 * q^56 + 8 * q^57 - 56 * q^58 - 16 * q^61 + 24 * q^62 - 208 * q^66 + 8 * q^67 + 96 * q^68 - 128 * q^69 + 112 * q^71 - 112 * q^72 + 8 * q^73 - 144 * q^76 + 8 * q^77 - 144 * q^78 + 64 * q^79 - 16 * q^81 + 168 * q^82 + 8 * q^83 - 16 * q^86 - 104 * q^87 + 96 * q^88 - 16 * q^91 + 88 * q^92 + 32 * q^93 + 32 * q^94 - 16 * q^96 - 32 * q^98 - 256 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)