Properties

Label 3267.1.be
Level $3267$
Weight $1$
Character orbit 3267.be
Rep. character $\chi_{3267}(245,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $24$
Newform subspaces $1$
Sturm bound $396$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3267 = 3^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3267.be (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 297 \)
Character field: \(\Q(\zeta_{90})\)
Newform subspaces: \( 1 \)
Sturm bound: \(396\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3267, [\chi])\).

Total New Old
Modular forms 312 216 96
Cusp forms 24 24 0
Eisenstein series 288 192 96

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q + 3 q^{5} + O(q^{10}) \) \( 24 q + 3 q^{5} + 3 q^{15} + 6 q^{20} + 3 q^{25} - 3 q^{27} - 3 q^{31} - 6 q^{36} - 3 q^{47} - 3 q^{48} - 3 q^{59} + 3 q^{64} - 24 q^{67} - 6 q^{75} - 36 q^{89} - 6 q^{93} - 6 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3267, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3267.1.be.a 3267.be 297.v $24$ $1.630$ \(\Q(\zeta_{45})\) $D_{18}$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(3\) \(0\) \(q+\zeta_{90}^{11}q^{3}+\zeta_{90}^{14}q^{4}+(-\zeta_{90}^{3}+\cdots)q^{5}+\cdots\)