Properties

Label 1375.1.bz
Level $1375$
Weight $1$
Character orbit 1375.bz
Rep. character $\chi_{1375}(54,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $20$
Newform subspaces $1$
Sturm bound $150$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1375 = 5^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1375.bz (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1375 \)
Character field: \(\Q(\zeta_{50})\)
Newform subspaces: \( 1 \)
Sturm bound: \(150\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1375, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 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

\( 20 q + 5 q^{5} + O(q^{10}) \) \( 20 q + 5 q^{5} - 20 q^{12} - 5 q^{25} - 5 q^{27} + 5 q^{48} + 5 q^{49} - 5 q^{59} - 5 q^{60} + 5 q^{67} + 5 q^{69} + 5 q^{81} - 5 q^{92} - 5 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1375, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1375.1.bz.a 1375.bz 1375.az $20$ $0.686$ \(\Q(\zeta_{50})\) $D_{50}$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(5\) \(0\) \(q+(\zeta_{50}^{7}-\zeta_{50}^{21})q^{3}-\zeta_{50}^{4}q^{4}-\zeta_{50}^{20}q^{5}+\cdots\)