Properties

Label 2520.1.ef
Level $2520$
Weight $1$
Character orbit 2520.ef
Rep. character $\chi_{2520}(739,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $4$
Sturm bound $576$
Trace bound $2$

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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.ef (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: \(2\)

Dimensions

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

Total New Old
Modular forms 56 20 36
Cusp forms 24 12 12
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 12 0 0 0

Trace form

\( 12q - 6q^{4} + O(q^{10}) \) \( 12q - 6q^{4} + 2q^{10} - 2q^{11} + 2q^{14} - 6q^{16} - 2q^{19} - 6q^{25} - 2q^{26} + 2q^{35} + 2q^{40} + 4q^{41} - 2q^{44} - 2q^{46} - 4q^{49} - 4q^{56} + 4q^{59} + 12q^{64} - 2q^{65} - 2q^{74} + 4q^{76} + 4q^{89} - 4q^{91} + 6q^{94} + O(q^{100}) \)

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.ef.a \(2\) \(1.258\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-10}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-q^{7}+\cdots\)
2520.1.ef.b \(2\) \(1.258\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-10}) \) None \(1\) \(0\) \(1\) \(2\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
2520.1.ef.c \(4\) \(1.258\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-10}) \) None \(-2\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots\)
2520.1.ef.d \(4\) \(1.258\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-10}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2520, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)