Properties

Label 2850.2.ce
Level $2850$
Weight $2$
Character orbit 2850.ce
Rep. character $\chi_{2850}(61,\cdot)$
Character field $\Q(\zeta_{45})$
Dimension $2400$
Sturm bound $1200$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2850.ce (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{45})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2850, [\chi])\).

Total New Old
Modular forms 14592 2400 12192
Cusp forms 14208 2400 11808
Eisenstein series 384 0 384

Trace form

\( 2400q - 24q^{7} + O(q^{10}) \) \( 2400q - 24q^{7} + 36q^{11} + 24q^{15} + 24q^{20} + 36q^{22} + 72q^{23} - 132q^{25} + 72q^{29} + 36q^{33} + 24q^{35} - 408q^{43} - 12q^{45} - 84q^{46} + 72q^{47} - 1224q^{49} - 72q^{53} + 180q^{55} - 24q^{57} + 72q^{59} - 12q^{60} - 144q^{61} - 48q^{62} + 300q^{64} - 48q^{67} - 24q^{68} - 48q^{69} - 24q^{70} - 24q^{71} - 72q^{73} + 96q^{77} - 48q^{78} + 96q^{79} + 96q^{82} + 108q^{83} - 24q^{84} + 144q^{85} - 36q^{87} + 144q^{89} + 96q^{92} + 192q^{94} - 12q^{95} - 264q^{97} - 288q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)