Properties

Label 775.1.d
Level $775$
Weight $1$
Character orbit 775.d
Rep. character $\chi_{775}(526,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 775.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(80\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(775, [\chi])\).

Total New Old
Modular forms 13 7 6
Cusp forms 7 4 3
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 4 0 0 0

Trace form

\( 4 q + q^{2} + 3 q^{4} + q^{7} - q^{8} + 4 q^{9} + O(q^{10}) \) \( 4 q + q^{2} + 3 q^{4} + q^{7} - q^{8} + 4 q^{9} - 5 q^{14} + 2 q^{16} + q^{18} - q^{19} - 2 q^{31} + 3 q^{36} - q^{38} - q^{41} - 2 q^{47} + 3 q^{49} - 7 q^{56} - q^{59} + q^{62} + q^{63} - 2 q^{64} - 2 q^{67} - q^{71} - q^{72} - 6 q^{76} + 4 q^{81} - q^{82} - 2 q^{94} + q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
775.1.d.a \(1\) \(0.387\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+q^{9}+q^{16}+2q^{19}-q^{31}+\cdots\)
775.1.d.b \(1\) \(0.387\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-31}) \) None \(1\) \(0\) \(0\) \(1\) \(q+q^{2}+q^{7}-q^{8}+q^{9}+q^{14}-q^{16}+\cdots\)
775.1.d.c \(2\) \(0.387\) \(\Q(\sqrt{3}) \) \(D_{6}\) \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+2q^{4}+\beta q^{7}-\beta q^{8}+q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(775, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)