Properties

Label 471.1.o
Level $471$
Weight $1$
Character orbit 471.o
Rep. character $\chi_{471}(14,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $12$
Newform subspaces $1$
Sturm bound $52$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 471.o (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 471 \)
Character field: \(\Q(\zeta_{26})\)
Newform subspaces: \( 1 \)
Sturm bound: \(52\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(471, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 12 12 0
Eisenstein series 24 24 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q - q^{3} - q^{4} - 2q^{7} - q^{9} + O(q^{10}) \) \( 12q - q^{3} - q^{4} - 2q^{7} - q^{9} + 12q^{12} - 2q^{13} - q^{16} - 2q^{19} - 2q^{21} - q^{25} - q^{27} - 2q^{28} - 2q^{31} - q^{36} - 2q^{37} - 2q^{39} - 2q^{43} - q^{48} - 3q^{49} - 2q^{52} - 2q^{57} - 2q^{61} - 2q^{63} - q^{64} - 2q^{67} - 2q^{73} - q^{75} - 2q^{76} - 2q^{79} - q^{81} - 2q^{84} + 9q^{91} - 2q^{93} + 11q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(471, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
471.1.o.a \(12\) \(0.235\) \(\Q(\zeta_{26})\) \(D_{13}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{26}^{3}q^{3}+\zeta_{26}^{10}q^{4}+(-\zeta_{26}-\zeta_{26}^{5}+\cdots)q^{7}+\cdots\)