Properties

Label 1375.1.d
Level $1375$
Weight $1$
Character orbit 1375.d
Rep. character $\chi_{1375}(1374,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $150$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1375 = 5^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1375.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(150\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 21 8 13
Cusp forms 11 8 3
Eisenstein series 10 0 10

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 8 q^{4} + 8 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{4} + 8 q^{9} - 4 q^{14} + 4 q^{16} - 4 q^{26} - 4 q^{34} + 8 q^{36} - 4 q^{44} + 8 q^{49} - 8 q^{56} - 4 q^{59} + 4 q^{64} - 4 q^{71} + 8 q^{81} - 4 q^{86} - 4 q^{91} + O(q^{100}) \)

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.d.a 1375.d 55.d $2$ $0.686$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-55}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots\)
1375.1.d.b 1375.d 55.d $2$ $0.686$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-55}) \) None \(1\) \(0\) \(0\) \(1\) \(q+(1-\beta )q^{2}+(1-\beta )q^{4}+\beta q^{7}+q^{8}+\cdots\)
1375.1.d.c 1375.d 55.d $4$ $0.686$ \(\Q(\zeta_{20})^+\) $D_{10}$ \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1375, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1375, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)