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

• Label: 2900.2.x
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.x
• Rep. character: $\chi_{2900}(289,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $304$
• Sturm bound: $900$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.x (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 725 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(900\)

Dimensions

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

	Total	New	Old
Modular forms	1824	304	1520
Cusp forms	1776	304	1472
Eisenstein series	48	0	48

Trace form

\( 304 q + 2 q^{5} - 80 q^{9} + 20 q^{23} - 30 q^{25} - 20 q^{33} - 12 q^{35} - 10 q^{45} - 344 q^{49} - 52 q^{51} + 30 q^{53} - 12 q^{59} + 66 q^{65} - 40 q^{67} + 18 q^{71} - 124 q^{81} + 5 q^{87} + 56 q^{91}+O(q^{100}) \)

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

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