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Properties

Label 1775.1.c
Level $1775$
Weight $1$
Character orbit 1775.c
Rep. character $\chi_{1775}(1774,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1775 = 5^{2} \cdot 71 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1775.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 355 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 26 8 18
Cusp forms 20 6 14
Eisenstein series 6 2 4

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + O(q^{10}) \) \( 6 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 2 q^{16} + 2 q^{19} - 6 q^{24} + 2 q^{29} - 2 q^{36} - 6 q^{49} + 8 q^{54} + 6 q^{71} - 10 q^{74} - 6 q^{76} + 2 q^{79} + 2 q^{81} - 4 q^{86} + 2 q^{89} + 2 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.c.a 1775.c 355.c $6$ $0.886$ 6.0.153664.1 $D_{7}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)

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

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