Properties

Label 2500.1.b
Level $2500$
Weight $1$
Character orbit 2500.b
Rep. character $\chi_{2500}(1251,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $375$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 42 20 22
Cusp forms 12 4 8
Eisenstein series 30 16 14

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

\( 4 q + 4 q^{4} + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{4} + 4 q^{9} + 4 q^{16} - 2 q^{26} - 2 q^{29} - 2 q^{34} + 4 q^{36} - 2 q^{41} + 4 q^{49} - 2 q^{61} + 4 q^{64} - 2 q^{74} + 4 q^{81} - 2 q^{89} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2500.1.b.a 2500.b 4.b $2$ $1.248$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+(1-\beta )q^{13}+\cdots\)
2500.1.b.b 2500.b 4.b $2$ $1.248$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}+(-1+\beta )q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2500, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2500, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)