↑

Properties

Label 900.6.be
Level $900$
Weight $6$
Character orbit 900.be
Rep. character $\chi_{900}(257,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $360$
Sturm bound $1080$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(900, [\chi])\).

Total New Old
Modular forms 3672 360 3312
Cusp forms 3528 360 3168
Eisenstein series 144 0 144

Trace form

\( 360 q + 2 q^{3} + O(q^{10}) \) \( 360 q + 2 q^{3} + 2280 q^{11} + 4360 q^{21} - 15816 q^{23} - 2854 q^{27} + 22046 q^{33} + 20028 q^{37} + 144360 q^{41} + 62322 q^{47} - 135040 q^{51} + 85874 q^{57} - 93480 q^{61} - 91594 q^{63} + 5514 q^{67} + 128064 q^{77} - 203260 q^{81} + 46740 q^{83} - 185608 q^{87} - 129360 q^{91} - 103252 q^{93} - 175842 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)