Properties

Label 1800.1.p
Level $1800$
Weight $1$
Character orbit 1800.p
Rep. character $\chi_{1800}(1099,\cdot)$
Character field $\Q$
Dimension $2$
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.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
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 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

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

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.p.a 1800.p 40.e $2$ $0.898$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) 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

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