Properties

Label 1800.1.cj
Level 1800
Weight 1
Character orbit cj
Rep. character \(\chi_{1800}(443,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 24
Newforms 3
Sturm bound 360
Trace bound 11

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.cj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 3 \)
Sturm bound: \(360\)
Trace bound: \(11\)

Dimensions

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

Total New Old
Modular forms 72 40 32
Cusp forms 24 24 0
Eisenstein series 48 16 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\(24q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 36q^{86} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.cj.a \(8\) \(0.898\) \(\Q(\zeta_{24})\) \(D_{6}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{11}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
1800.1.cj.b \(8\) \(0.898\) \(\Q(\zeta_{24})\) \(D_{6}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
1800.1.cj.c \(8\) \(0.898\) \(\Q(\zeta_{24})\) \(D_{6}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)