Properties

Label 2520.1.fw
Level $2520$
Weight $1$
Character orbit 2520.fw
Rep. character $\chi_{2520}(349,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $576$
Trace bound $15$

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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.fw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2520 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(15\)

Dimensions

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

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

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

\( 16 q + 8 q^{4} + O(q^{10}) \) \( 16 q + 8 q^{4} - 8 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{30} - 8 q^{39} + 8 q^{49} - 4 q^{50} + 8 q^{56} - 4 q^{60} - 16 q^{64} + 4 q^{65} - 16 q^{81} + 8 q^{95} + O(q^{100}) \)

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.fw.a 2520.fw 2520.ew $8$ $1.258$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{9}q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
2520.1.fw.b 2520.fw 2520.ew $8$ $1.258$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{2}q^{2}-\zeta_{24}^{9}q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)