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Properties

Label 1331.1.d
Level $1331$
Weight $1$
Character orbit 1331.d
Rep. character $\chi_{1331}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $20$
Newform subspaces $1$
Sturm bound $121$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1331 = 11^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1331.d (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(121\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1331, [\chi])\).

Total New Old
Modular forms 64 20 44
Cusp forms 20 20 0
Eisenstein series 44 0 44

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + q^{3} - 5 q^{4} + q^{5} - 4 q^{9} + O(q^{10}) \) \( 20 q + q^{3} - 5 q^{4} + q^{5} - 4 q^{9} - 4 q^{12} + 2 q^{15} - 5 q^{16} + q^{20} - 4 q^{23} - 4 q^{25} + 2 q^{27} + q^{31} - 4 q^{36} + q^{37} - 12 q^{45} + q^{47} + q^{48} - 5 q^{49} + q^{53} + q^{59} + 2 q^{60} - 5 q^{64} - 4 q^{67} + 2 q^{69} + q^{71} + 3 q^{75} + q^{80} - 3 q^{81} - 4 q^{89} + q^{92} + 2 q^{93} + q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1331, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1331.1.d.a 1331.d 11.d $20$ $0.664$ 20.0.\(\cdots\).1 $D_{11}$ \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(1\) \(0\) \(q-\beta _{13}q^{3}+\beta _{9}q^{4}+(\beta _{8}+\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots\)