Properties

Label 1800.1.p
Level 1800
Weight 1
Character orbit p
Rep. character \(\chi_{1800}(1099,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
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.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 40 \)
Character field: \(\Q\)
Newforms: \( 1 \)
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 36 4 32
Cusp forms 12 2 10
Eisenstein series 24 2 22

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{4} + O(q^{10}) \) \( 2q - 2q^{4} + 2q^{11} + 2q^{16} + 2q^{19} + 2q^{34} + 2q^{41} - 2q^{44} - 2q^{49} + 4q^{59} - 2q^{64} - 2q^{76} - 4q^{86} - 2q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1800, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1800.1.p.a \(2\) \(0.898\) \(\Q(\sqrt{-1}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{11}+q^{16}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)