Space of modular forms of level 2600, weight 2, and Character 2600.di

• Label: 2600.2.di
• Level: $2600$
• Weight: $2$
• Character orbit: 2600.di
• Rep. character: $\chi_{2600}(43,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $992$
• Sturm bound: $840$

Defining parameters

Level:	\( N \)	\(=\)	\( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2600.di (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 520 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2600, [\chi])\).

	Total	New	Old
Modular forms	1728	1024	704
Cusp forms	1632	992	640
Eisenstein series	96	32	64

Trace form

992 * q + 6 * q^2 + 4 * q^3 - 12 * q^6 - 24 * q^11 + 36 * q^12 + 12 * q^16 + 8 * q^22 + 8 * q^26 + 40 * q^27 + 6 * q^28 + 36 * q^32 + 12 * q^33 - 68 * q^36 - 24 * q^41 - 44 * q^42 - 28 * q^43 - 12 * q^46 + 16 * q^48 - 32 * q^51 - 6 * q^52 - 36 * q^56 + 78 * q^58 + 4 * q^62 - 192 * q^66 + 12 * q^67 - 8 * q^68 + 54 * q^72 - 12 * q^76 + 116 * q^78 + 424 * q^81 + 42 * q^82 - 70 * q^88 + 112 * q^91 - 60 * q^92 + 12 * q^97 - 66 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)