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

• Label: 2900.2.cj
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.cj
• Rep. character: $\chi_{2900}(121,\cdot)$
• Character field: $\Q(\zeta_{70})$
• Dimension: $1776$
• Sturm bound: $900$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.cj (of order \(70\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 725 \)
Character field:			\(\Q(\zeta_{70})\)
Sturm bound:			\(900\)

Dimensions

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

	Total	New	Old
Modular forms	10944	1776	9168
Cusp forms	10656	1776	8880
Eisenstein series	288	0	288

Trace form

1776 * q - 8 * q^7 - 70 * q^9 - 12 * q^13 + 14 * q^15 - 12 * q^23 + 63 * q^27 + 10 * q^29 - 8 * q^33 + 30 * q^35 - 42 * q^37 - 28 * q^43 - 28 * q^45 - 256 * q^49 - 52 * q^51 + 48 * q^53 - 56 * q^55 + 48 * q^57 + 96 * q^59 + 84 * q^61 - 104 * q^63 - 64 * q^65 + 8 * q^67 - 45 * q^71 - 28 * q^73 - 42 * q^77 + 138 * q^81 + 56 * q^83 + 14 * q^85 - 71 * q^87 - 70 * q^91 + 4 * q^93 + 112 * q^97

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

\( S_{2}^{\mathrm{old}}(2900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1450, [\chi])\)\(^{\oplus 2}\)