Properties

Label 1800.1.ba
Level $1800$
Weight $1$
Character orbit 1800.ba
Rep. character $\chi_{1800}(499,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $3$
Sturm bound $360$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1800.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(360\)
Trace bound: \(9\)

Dimensions

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

Total New Old
Modular forms 36 20 16
Cusp forms 12 12 0
Eisenstein series 24 8 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q + 6q^{4} + O(q^{10}) \) \( 12q + 6q^{4} - 6q^{16} + 6q^{49} + 12q^{51} + 6q^{54} - 6q^{59} - 12q^{64} - 6q^{66} + 6q^{86} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1800.1.ba.a \(4\) \(0.898\) \(\Q(\zeta_{12})\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
1800.1.ba.b \(4\) \(0.898\) \(\Q(\zeta_{12})\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
1800.1.ba.c \(4\) \(0.898\) \(\Q(\zeta_{12})\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+q^{6}+\cdots\)