Properties

Label 900.3.bm
Level $900$
Weight $3$
Character orbit 900.bm
Rep. character $\chi_{900}(41,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $480$
Sturm bound $540$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.bm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 2928 480 2448
Cusp forms 2832 480 2352
Eisenstein series 96 0 96

Trace form

\( 480q - 2q^{3} + 36q^{5} + 10q^{9} + O(q^{10}) \) \( 480q - 2q^{3} + 36q^{5} + 10q^{9} - 45q^{15} - 60q^{21} - 144q^{23} + 12q^{25} + 103q^{27} + 30q^{31} + 19q^{33} + 84q^{37} - 220q^{39} - 521q^{45} - 279q^{47} - 1680q^{49} + 170q^{51} - 90q^{55} + 582q^{57} - 135q^{59} + 79q^{63} - 81q^{65} + 117q^{67} - 50q^{69} + 562q^{75} + 792q^{77} - 120q^{79} + 250q^{81} + 360q^{83} - 48q^{85} + 401q^{87} + 402q^{93} - 36q^{95} + 294q^{97} - 210q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)