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Properties

Label 2600.1.bk
Level $2600$
Weight $1$
Character orbit 2600.bk
Rep. character $\chi_{2600}(707,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $420$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2600.bk (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(420\)
Trace bound: \(13\)

Dimensions

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

Total New Old
Modular forms 28 12 16
Cusp forms 4 4 0
Eisenstein series 24 8 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - 4 q^{4} + O(q^{10}) \) \( 4 q - 4 q^{4} - 4 q^{11} + 4 q^{16} - 4 q^{19} + 4 q^{41} + 4 q^{44} - 4 q^{46} - 4 q^{49} + 4 q^{59} - 4 q^{64} + 4 q^{76} - 4 q^{81} - 4 q^{89} + 4 q^{99} + O(q^{100}) \)

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.bk.a 2600.bk 520.ak $2$ $1.298$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-iq^{9}+(-1+i+\cdots)q^{11}+\cdots\)
2600.1.bk.b 2600.bk 520.ak $2$ $1.298$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}-iq^{9}+(-1+i+\cdots)q^{11}+\cdots\)