Properties

Label 1800.1.bt
Level 1800
Weight 1
Character orbit bt
Rep. character \(\chi_{1800}(271,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 0
Newforms 0
Sturm bound 360
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1800.bt (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 0 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).

Total New Old
Modular forms 96 0 96
Cusp forms 32 0 32
Eisenstein series 64 0 64

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 0 0

Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)