Properties

Label 1375.1.ch
Level $1375$
Weight $1$
Character orbit 1375.ch
Rep. character $\chi_{1375}(21,\cdot)$
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.ch (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

\( 20q - 5q^{5} + O(q^{10}) \) \( 20q - 5q^{5} + 20q^{12} - 5q^{25} - 5q^{27} - 5q^{48} - 5q^{49} - 5q^{59} - 5q^{60} - 5q^{67} - 5q^{69} - 5q^{81} - 5q^{92} - 10q^{93} - 5q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1375.1.ch.a \(20\) \(0.686\) \(\Q(\zeta_{50})\) \(D_{25}\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-5\) \(0\) \(q+(\zeta_{50}^{4}+\zeta_{50}^{18})q^{3}-\zeta_{50}^{21}q^{4}+\cdots\)