Properties

Label 3040.1.b
Level $3040$
Weight $1$
Character orbit 3040.b
Rep. character $\chi_{3040}(1329,\cdot)$
Character field $\Q$
Dimension $8$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q\)
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 12 36
Cusp forms 32 8 24
Eisenstein series 16 4 12

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

\( 8 q - 8 q^{9} + O(q^{10}) \) \( 8 q - 8 q^{9} - 8 q^{25} + 8 q^{49} + 8 q^{81} - 8 q^{95} + O(q^{100}) \)

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.b.a 3040.b 760.b $8$ $1.517$ \(\Q(\zeta_{16})\) $D_{8}$ \(\Q(\sqrt{-95}) \) None 760.1.b.a \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}+\zeta_{16}^{4}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3040, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3040, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1520, [\chi])\)\(^{\oplus 2}\)