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Properties

Label 2564.1.d
Level $2564$
Weight $1$
Character orbit 2564.d
Rep. character $\chi_{2564}(2563,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $4$
Sturm bound $321$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2564 = 2^{2} \cdot 641 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2564.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2564 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(321\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2564, [\chi])\).

Total New Old
Modular forms 15 15 0
Cusp forms 13 13 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 13 0 0 0

Trace form

\( 13 q - q^{2} + 13 q^{4} - 2 q^{5} - q^{8} + 11 q^{9} + O(q^{10}) \) \( 13 q - q^{2} + 13 q^{4} - 2 q^{5} - q^{8} + 11 q^{9} - 2 q^{10} - 2 q^{13} + 13 q^{16} - 3 q^{18} - 2 q^{20} + 11 q^{25} - 2 q^{26} - q^{32} + 11 q^{36} - 2 q^{37} - 2 q^{40} - 6 q^{45} + 13 q^{49} - 3 q^{50} - 2 q^{52} - 4 q^{57} + 13 q^{64} - 4 q^{65} - 4 q^{69} - 3 q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{80} + 9 q^{81} - 2 q^{89} - 6 q^{90} - 4 q^{93} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2564, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2564.1.d.a 2564.d 2564.d $1$ $1.280$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-641}) \) \(\Q(\sqrt{641}) \) 2564.1.d.a \(-1\) \(0\) \(-2\) \(0\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}-q^{9}+2q^{10}+\cdots\)
2564.1.d.b 2564.d 2564.d $3$ $1.280$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-641}) \) None 2564.1.d.b \(3\) \(-1\) \(-1\) \(0\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
2564.1.d.c 2564.d 2564.d $3$ $1.280$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-641}) \) None 2564.1.d.b \(3\) \(1\) \(-1\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
2564.1.d.d 2564.d 2564.d $6$ $1.280$ \(\Q(\zeta_{28})^+\) $D_{14}$ \(\Q(\sqrt{-641}) \) None 2564.1.d.d \(-6\) \(0\) \(2\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)