Properties

Label 3200.1.m
Level $3200$
Weight $1$
Character orbit 3200.m
Rep. character $\chi_{3200}(193,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $5$
Sturm bound $480$
Trace bound $41$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3200.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(480\)
Trace bound: \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3200, [\chi])\).

Total New Old
Modular forms 148 20 128
Cusp forms 52 20 32
Eisenstein series 96 0 96

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + O(q^{10}) \) \( 20 q - 4 q^{17} - 8 q^{41} + 4 q^{73} - 20 q^{81} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3200, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3200.1.m.a 3200.m 40.i $2$ $1.597$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+(-1-i)q^{13}+(-1-i)q^{17}+\cdots\)
3200.1.m.b 3200.m 40.i $2$ $1.597$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+(1+i)q^{13}+(-1-i)q^{17}+\cdots\)
3200.1.m.c 3200.m 40.i $4$ $1.597$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\zeta_{8}q^{23}-q^{41}+\cdots\)
3200.1.m.d 3200.m 40.i $4$ $1.597$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}-3\zeta_{8}^{2}q^{9}+2\zeta_{8}q^{27}+q^{41}+\cdots\)
3200.1.m.e 3200.m 40.i $8$ $1.597$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{4}-\zeta_{24}^{8})q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 2}\)