Properties

Label 1775.1.d
Level $1775$
Weight $1$
Character orbit 1775.d
Rep. character $\chi_{1775}(851,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $180$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1775 = 5^{2} \cdot 71 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1775.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 71 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1775, [\chi])\).

Total New Old
Modular forms 25 13 12
Cusp forms 19 10 9
Eisenstein series 6 3 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q + q^{2} + q^{3} + 9 q^{4} - 2 q^{6} + 2 q^{8} + 9 q^{9} + O(q^{10}) \) \( 10 q + q^{2} + q^{3} + 9 q^{4} - 2 q^{6} + 2 q^{8} + 9 q^{9} + 3 q^{12} + 8 q^{16} - 4 q^{18} - q^{19} - 11 q^{24} + 2 q^{27} - q^{29} + 3 q^{32} + 6 q^{36} + q^{37} - 5 q^{38} + q^{43} - 2 q^{48} + 10 q^{49} - 4 q^{54} + 2 q^{57} + 2 q^{58} + 7 q^{64} - 4 q^{71} - q^{72} + q^{73} - 9 q^{74} - 3 q^{76} - q^{79} + 8 q^{81} + q^{83} - 2 q^{86} - 5 q^{87} - q^{89} - 13 q^{96} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1775, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1775.1.d.a 1775.d 71.b $1$ $0.886$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-355}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-q^{9}+q^{16}+2q^{19}+2q^{29}+\cdots\)
1775.1.d.b 1775.d 71.b $3$ $0.886$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-71}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1775.1.d.c 1775.d 71.b $6$ $0.886$ \(\Q(\zeta_{28})^+\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(1-2\beta _{2}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1775, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1775, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(71, [\chi])\)\(^{\oplus 3}\)