Properties

Label 1800.1.cr
Level $1800$
Weight $1$
Character orbit 1800.cr
Rep. character $\chi_{1800}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $16$
Newform subspaces $1$
Sturm bound $360$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1800.cr (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
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 80 32 48
Cusp forms 16 16 0
Eisenstein series 64 16 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q + 4 q^{7} + O(q^{10}) \) \( 16 q + 4 q^{7} - 4 q^{10} + 4 q^{16} - 4 q^{22} - 16 q^{28} + 4 q^{55} + 4 q^{58} + 4 q^{70} - 4 q^{73} - 4 q^{88} - 16 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1800.1.cr.a 1800.cr 200.x $16$ $0.898$ \(\Q(\zeta_{40})\) $D_{20}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{40}^{19}q^{2}-\zeta_{40}^{18}q^{4}+\zeta_{40}^{9}q^{5}+\cdots\)