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

• Label: 2900.2.cf
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.cf
• Rep. character: $\chi_{2900}(251,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $3348$
• Sturm bound: $900$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.cf (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
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	3492	2052
Cusp forms	5256	3348	1908
Eisenstein series	288	144	144

Trace form

3348 * q + 14 * q^2 + 14 * q^4 - 42 * q^6 + 8 * q^8 + 28 * q^9 + 28 * q^13 + 2 * q^14 - 10 * q^16 + 14 * q^17 - 68 * q^21 + 14 * q^22 - 2 * q^24 - 48 * q^26 + 32 * q^29 + 4 * q^32 + 28 * q^33 + 14 * q^34 - 90 * q^36 + 18 * q^37 + 14 * q^38 - 82 * q^41 + 14 * q^42 - 2 * q^44 + 8 * q^46 - 48 * q^48 + 490 * q^49 + 94 * q^52 + 68 * q^53 + 124 * q^54 + 8 * q^56 - 102 * q^58 - 54 * q^61 + 112 * q^62 + 140 * q^64 + 100 * q^66 - 40 * q^68 - 4 * q^69 + 120 * q^72 + 58 * q^73 + 24 * q^74 - 38 * q^76 + 44 * q^77 - 26 * q^78 + 322 * q^81 - 10 * q^82 - 184 * q^84 - 96 * q^88 - 50 * q^89 + 14 * q^92 + 28 * q^93 - 14 * q^94 - 84 * q^96 - 84 * q^97 - 52 * 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

\( S_{2}^{\mathrm{old}}(2900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)