Properties

Label 2520.1.ek
Level $2520$
Weight $1$
Character orbit 2520.ek
Rep. character $\chi_{2520}(829,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $4$
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.ek (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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 40 16 24
Cusp forms 8 8 0
Eisenstein series 32 8 24

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

\( 8q - 4q^{4} + O(q^{10}) \) \( 8q - 4q^{4} - 6q^{10} - 4q^{16} + 2q^{25} - 12q^{31} + 6q^{40} - 4q^{49} + 8q^{64} - 2q^{70} - 4q^{79} + O(q^{100}) \)

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.ek.a \(2\) \(1.258\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-6}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{7}+\cdots\)
2520.1.ek.b \(2\) \(1.258\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-6}) \) None \(-1\) \(0\) \(2\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+q^{8}+\cdots\)
2520.1.ek.c \(2\) \(1.258\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-6}) \) None \(1\) \(0\) \(-2\) \(1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{5}+\zeta_{6}q^{7}-q^{8}+\cdots\)
2520.1.ek.d \(2\) \(1.258\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-6}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{7}+\cdots\)