Properties

Label 1600.1.bd
Level $1600$
Weight $1$
Character orbit 1600.bd
Rep. character $\chi_{1600}(31,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $16$
Newform subspaces $2$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1600.bd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 64 16 48
Cusp forms 16 16 0
Eisenstein series 48 0 48

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

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

Trace form

\( 16 q + 8 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{9} - 12 q^{17} + 4 q^{25} + 12 q^{33} - 4 q^{41} + 16 q^{57} + 4 q^{65} - 8 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1600.1.bd.a 1600.bd 200.n $8$ $0.799$ \(\Q(\zeta_{20})\) $A_{5}$ None None 1600.1.bd.a \(0\) \(-6\) \(0\) \(0\) \(q+(-1+\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}+\zeta_{20}^{5}q^{7}+\cdots\)
1600.1.bd.b 1600.bd 200.n $8$ $0.799$ \(\Q(\zeta_{20})\) $A_{5}$ None None 1600.1.bd.a \(0\) \(6\) \(0\) \(0\) \(q+(1-\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}-\zeta_{20}^{5}q^{7}+\cdots\)

Additional information

This is the first newspace containing multiple newforms with projective image $A_5$.