Properties

Label 147.1.l
Level $147$
Weight $1$
Character orbit 147.l
Rep. character $\chi_{147}(8,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $6$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 147.l (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(147, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

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

\( 6q - q^{3} - q^{4} - q^{7} - q^{9} + O(q^{10}) \) \( 6q - q^{3} - q^{4} - q^{7} - q^{9} - q^{12} - 2q^{13} - q^{16} - 2q^{19} - q^{21} - q^{25} - q^{27} - q^{28} - 2q^{31} - q^{36} + 5q^{37} + 5q^{39} - 2q^{43} + 6q^{48} - q^{49} + 5q^{52} - 2q^{57} + 5q^{61} + 6q^{63} - q^{64} - 2q^{67} - 2q^{73} - q^{75} - 2q^{76} - 2q^{79} - q^{81} - q^{84} - 2q^{91} - 2q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
147.1.l.a \(6\) \(0.073\) \(\Q(\zeta_{14})\) \(D_{7}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots\)