↑

Properties

Label 900.4.bq
Level $900$
Weight $4$
Character orbit 900.bq
Rep. character $\chi_{900}(169,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $720$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 900.bq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(900, [\chi])\).

Total New Old
Modular forms 4368 720 3648
Cusp forms 4272 720 3552
Eisenstein series 96 0 96

Trace form

\( 720 q + 16 q^{5} - 32 q^{9} + O(q^{10}) \) \( 720 q + 16 q^{5} - 32 q^{9} + 44 q^{11} + 328 q^{15} - 48 q^{21} + 288 q^{25} - 330 q^{27} - 348 q^{29} + 36 q^{31} + 800 q^{33} + 304 q^{35} - 1012 q^{39} + 656 q^{41} - 426 q^{45} - 950 q^{47} + 17640 q^{49} - 848 q^{51} - 1008 q^{55} - 1206 q^{59} - 1210 q^{63} + 1622 q^{65} + 1530 q^{67} + 220 q^{69} - 1532 q^{71} - 2910 q^{75} + 2720 q^{77} + 252 q^{79} - 1032 q^{81} - 140 q^{83} - 828 q^{85} + 10350 q^{87} + 8672 q^{89} - 36 q^{95} + 1364 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)