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

• Label: 2900.2.cb
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.cb
• Rep. character: $\chi_{2900}(207,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $3192$
• Sturm bound: $900$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.cb (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 580 \)
Character field:			\(\Q(\zeta_{28})\)
Sturm bound:			\(900\)

Dimensions

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

	Total	New	Old
Modular forms	5544	3288	2256
Cusp forms	5256	3192	2064
Eisenstein series	288	96	192

Trace form

3192 * q + 14 * q^2 - 20 * q^6 + 14 * q^8 + 16 * q^13 - 20 * q^16 - 84 * q^18 - 56 * q^21 + 2 * q^22 - 28 * q^26 + 40 * q^28 + 14 * q^32 + 12 * q^33 - 52 * q^36 + 28 * q^37 + 60 * q^38 + 54 * q^42 + 126 * q^48 + 116 * q^52 + 10 * q^53 - 112 * q^56 + 72 * q^57 + 150 * q^58 - 56 * q^61 + 32 * q^62 + 308 * q^66 + 168 * q^68 + 14 * q^72 - 154 * q^73 - 28 * q^76 + 28 * q^77 + 30 * q^78 + 268 * q^81 - 30 * q^82 - 152 * q^86 - 56 * q^88 - 22 * q^92 - 4 * q^93 + 124 * q^96 + 98 * q^97 + 14 * 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

\( S_{2}^{\mathrm{old}}(2900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)