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Properties

Label 3364.1.d
Level $3364$
Weight $1$
Character orbit 3364.d
Rep. character $\chi_{3364}(3363,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $435$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3364 = 2^{2} \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3364.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 116 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(435\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3364, [\chi])\).

Total New Old
Modular forms 40 32 8
Cusp forms 10 6 4
Eisenstein series 30 26 4

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - 6 q^{4} + 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 6 q - 6 q^{4} + 2 q^{5} - 6 q^{9} + 2 q^{13} + 6 q^{16} - 2 q^{20} + 4 q^{25} + 2 q^{34} + 6 q^{36} - 2 q^{45} + 6 q^{49} - 2 q^{52} - 2 q^{53} - 6 q^{64} - 4 q^{65} - 2 q^{74} + 2 q^{80} + 6 q^{81} - 2 q^{82} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3364, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3364.1.d.a 3364.d 116.d $6$ $1.679$ 6.0.153664.1 $D_{7}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{5}q^{2}-q^{4}+\beta _{4}q^{5}-\beta _{5}q^{8}-q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3364, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3364, [\chi]) \cong \)