Properties

Label 2500.1.n
Level $2500$
Weight $1$
Character orbit 2500.n
Rep. character $\chi_{2500}(99,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $40$
Newform subspaces $1$
Sturm bound $375$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2500 = 2^{2} \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2500.n (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 500 \)
Character field: \(\Q(\zeta_{50})\)
Newform subspaces: \( 1 \)
Sturm bound: \(375\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2500, [\chi])\).

Total New Old
Modular forms 240 160 80
Cusp forms 40 40 0
Eisenstein series 200 120 80

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 0 0 0

Trace form

\( 40 q + O(q^{10}) \) \( 40 q + 10 q^{34} + 10 q^{49} + 10 q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2500, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2500.1.n.a $40$ $1.248$ \(\Q(\zeta_{100})\) $D_{25}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{100}q^{2}+\zeta_{100}^{2}q^{4}-\zeta_{100}^{3}q^{8}+\zeta_{100}^{14}q^{9}+\cdots\)