Properties

Label 2520.1.hf
Level $2520$
Weight $1$
Character orbit 2520.hf
Rep. character $\chi_{2520}(293,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $32$
Newform subspaces $2$
Sturm bound $576$
Trace bound $14$

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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.hf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2520 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(14\)

Dimensions

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

Total New Old
Modular forms 64 64 0
Cusp forms 32 32 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32q + O(q^{10}) \) \( 32q + 16q^{16} - 8q^{18} - 24q^{23} - 8q^{57} + 8q^{60} + 8q^{63} - 24q^{65} - 16q^{72} - 16q^{78} - 24q^{92} + O(q^{100}) \)

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.hf.a \(16\) \(1.258\) \(\Q(\zeta_{48})\) \(D_{24}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{2}q^{2}+\zeta_{48}^{15}q^{3}+\zeta_{48}^{4}q^{4}+\cdots\)
2520.1.hf.b \(16\) \(1.258\) \(\Q(\zeta_{48})\) \(D_{24}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{14}q^{2}+\zeta_{48}^{15}q^{3}-\zeta_{48}^{4}q^{4}+\cdots\)