Properties

Label 2600.1.b
Level $2600$
Weight $1$
Character orbit 2600.b
Rep. character $\chi_{2600}(1299,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $420$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2600.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(420\)
Trace bound: \(6\)

Dimensions

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

Total New Old
Modular forms 28 8 20
Cusp forms 16 4 12
Eisenstein series 12 4 8

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

\( 4 q - 4 q^{4} + O(q^{10}) \) \( 4 q - 4 q^{4} + 4 q^{14} + 4 q^{16} + 4 q^{26} + 4 q^{51} - 4 q^{56} - 4 q^{64} + 4 q^{74} - 4 q^{81} - 4 q^{91} + 4 q^{94} + O(q^{100}) \)

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.b.a 2600.b 520.b $2$ $1.298$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
2600.1.b.b 2600.b 520.b $2$ $1.298$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{7}-iq^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2600, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)