Properties

Label 2520.1.eq
Level $2520$
Weight $1$
Character orbit 2520.eq
Rep. character $\chi_{2520}(899,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
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.eq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 840 \)
Character field: \(\Q(\zeta_{6})\)
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 48 16 32
Cusp forms 16 16 0
Eisenstein series 32 0 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q + 8q^{4} + O(q^{10}) \) \( 16q + 8q^{4} - 8q^{16} - 8q^{25} - 16q^{64} - 8q^{91} - 24q^{94} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2520.1.eq.a \(8\) \(1.258\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{4}q^{5}+\cdots\)
2520.1.eq.b \(8\) \(1.258\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+\zeta_{24}^{4}q^{5}+\cdots\)