Properties

Label 3040.1.cn
Level $3040$
Weight $1$
Character orbit 3040.cn
Rep. character $\chi_{3040}(189,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $32$
Newform subspaces $1$
Sturm bound $480$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3040.cn (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3040 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(480\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3040, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 32 32 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 32 0 0 0

Trace form

\( 32 q + O(q^{10}) \) \( 32 q - 32 q^{66} + 32 q^{80} - 32 q^{95} - 32 q^{96} - 32 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3040, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3040.1.cn.a 3040.cn 3040.bn $32$ $1.517$ \(\Q(\zeta_{64})\) $D_{32}$ \(\Q(\sqrt{-95}) \) None 3040.1.cn.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{64}^{27}q^{2}+(-\zeta_{64}^{25}-\zeta_{64}^{31}+\cdots)q^{3}+\cdots\)