Properties

Label 2520.1.b
Level $2520$
Weight $1$
Character orbit 2520.b
Rep. character $\chi_{2520}(1259,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2520.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 840 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2520, [\chi])\).

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

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 8 q^{4} + O(q^{10}) \) \( 8 q - 8 q^{4} + 8 q^{16} + 8 q^{25} - 8 q^{64} + 8 q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2520, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2520.1.b.a 2520.b 840.b $4$ $1.258$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}-q^{5}-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{8}+\cdots\)
2520.1.b.b 2520.b 840.b $4$ $1.258$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}^{2}q^{2}-q^{4}+q^{5}-\zeta_{8}q^{7}+\zeta_{8}^{2}q^{8}+\cdots\)