Space of modular forms of level 2900, weight 2, and Character 2900.bq

• Label: 2900.2.bq
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.bq
• Rep. character: $\chi_{2900}(523,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $3360$
• Sturm bound: $900$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.bq (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2900, [\chi])\).

	Total	New	Old
Modular forms	3632	3360	272
Cusp forms	3568	3360	208
Eisenstein series	64	0	64

Trace form

3360 * q + 12 * q^8 + 16 * q^10 + 16 * q^12 - 20 * q^20 - 4 * q^22 - 12 * q^28 + 24 * q^30 + 20 * q^32 - 48 * q^38 - 104 * q^40 - 200 * q^42 - 208 * q^48 - 60 * q^50 - 56 * q^52 + 48 * q^53 - 260 * q^54 + 32 * q^57 - 120 * q^60 - 80 * q^62 - 60 * q^64 + 32 * q^65 - 8 * q^68 + 20 * q^70 + 20 * q^72 - 48 * q^77 - 24 * q^78 - 20 * q^80 + 840 * q^81 + 144 * q^82 - 48 * q^85 + 20 * q^88 + 316 * q^90 + 176 * q^92 - 176 * q^93 + 320 * q^94 - 40 * q^96 + 332 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)