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Properties

Label 1441.1.u
Level $1441$
Weight $1$
Character orbit 1441.u
Rep. character $\chi_{1441}(130,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $20$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1441.u (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1441 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1441, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

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

\( 20 q - 5 q^{4} - 5 q^{9} + O(q^{10}) \) \( 20 q - 5 q^{4} - 5 q^{9} - 5 q^{16} - 5 q^{25} + 20 q^{33} + 15 q^{35} - 5 q^{36} - 10 q^{39} - 10 q^{45} - 5 q^{49} - 10 q^{53} - 10 q^{63} - 5 q^{64} - 10 q^{75} - 5 q^{81} - 10 q^{89} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1441, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1441.1.u.a 1441.u 1441.u $20$ $0.719$ \(\Q(\zeta_{50})\) $D_{25}$ \(\Q(\sqrt{-131}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}+\zeta_{50}^{10}q^{4}+\cdots\)