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Properties

Label 2600.1.ck
Level $2600$
Weight $1$
Character orbit 2600.ck
Rep. character $\chi_{2600}(571,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $24$
Newform subspaces $4$
Sturm bound $420$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2600.ck (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2600 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 4 \)
Sturm bound: \(420\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2600, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q - 6 q^{4} - 6 q^{9} + O(q^{10}) \) \( 24 q - 6 q^{4} - 6 q^{9} - 6 q^{16} + 24 q^{26} - 12 q^{27} - 6 q^{30} - 6 q^{35} - 6 q^{36} - 12 q^{42} + 24 q^{49} - 12 q^{51} + 18 q^{62} - 6 q^{64} - 6 q^{75} - 6 q^{81} + 24 q^{90} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2600.1.ck.a 2600.ck 2600.bk $4$ $1.298$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-26}) \) None \(-1\) \(-2\) \(4\) \(-2\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{3}-\zeta_{10}q^{4}+q^{5}+\cdots\)
2600.1.ck.b 2600.ck 2600.bk $4$ $1.298$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-26}) \) None \(1\) \(-2\) \(-4\) \(2\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{3}-\zeta_{10}q^{4}-q^{5}+\cdots\)
2600.1.ck.c 2600.ck 2600.bk $8$ $1.298$ \(\Q(\zeta_{15})\) $D_{15}$ \(\Q(\sqrt{-26}) \) None \(-2\) \(2\) \(-4\) \(2\) \(q-\zeta_{30}^{9}q^{2}+\zeta_{30}^{3}q^{3}-\zeta_{30}^{3}q^{4}+\cdots\)
2600.1.ck.d 2600.ck 2600.bk $8$ $1.298$ \(\Q(\zeta_{15})\) $D_{15}$ \(\Q(\sqrt{-26}) \) None \(2\) \(2\) \(4\) \(-2\) \(q+\zeta_{30}^{9}q^{2}+\zeta_{30}^{3}q^{3}-\zeta_{30}^{3}q^{4}+\cdots\)