Properties

Label 1600.1.b
Level $1600$
Weight $1$
Character orbit 1600.b
Rep. character $\chi_{1600}(1151,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1600.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1600, [\chi])\).

Total New Old
Modular forms 40 4 36
Cusp forms 4 1 3
Eisenstein series 36 3 33

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q + q^{9} + O(q^{10}) \) \( q + q^{9} + 2 q^{29} - 2 q^{41} + q^{49} + 2 q^{61} + q^{81} - 2 q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1600.1.b.a 1600.b 4.b $1$ $0.799$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}+2q^{29}-2q^{41}+q^{49}+2q^{61}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1600, [\chi]) \cong \)