Properties

Label 1600.1.m
Level $1600$
Weight $1$
Character orbit 1600.m
Rep. character $\chi_{1600}(993,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $4$
Sturm bound $240$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1600.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(19\)

Dimensions

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

Total New Old
Modular forms 84 12 72
Cusp forms 12 12 0
Eisenstein series 72 0 72

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

\( 12 q + O(q^{10}) \) \( 12 q - 12 q^{81} + O(q^{100}) \)

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.m.a 1600.m 40.i $2$ $0.799$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{5}) \) 1600.1.m.a \(0\) \(0\) \(0\) \(0\) \(q-i q^{9}-2 i q^{11}-2 q^{19}+2 q^{41}+\cdots\)
1600.1.m.b 1600.m 40.i $2$ $0.799$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{5}) \) 1600.1.m.a \(0\) \(0\) \(0\) \(0\) \(q-i q^{9}+2 i q^{11}+2 q^{19}+2 q^{41}+\cdots\)
1600.1.m.c 1600.m 40.i $4$ $0.799$ \(\Q(i, \sqrt{6})\) $D_{6}$ \(\Q(\sqrt{-2}) \) None 1600.1.m.c \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+2\beta _{2}q^{9}-\beta _{2}q^{11}-\beta _{1}q^{17}+\cdots\)
1600.1.m.d 1600.m 40.i $4$ $0.799$ \(\Q(i, \sqrt{6})\) $D_{6}$ \(\Q(\sqrt{-2}) \) None 1600.1.m.c \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+2\beta _{2}q^{9}+\beta _{2}q^{11}+\beta _{1}q^{17}+\cdots\)