Properties

Label 1323.1.br
Level $1323$
Weight $1$
Character orbit 1323.br
Rep. character $\chi_{1323}(53,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $12$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1323.br (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1323, [\chi])\).

Total New Old
Modular forms 84 12 72
Cusp forms 12 12 0
Eisenstein series 72 0 72

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

\( 12 q + q^{4} - 2 q^{7} + O(q^{10}) \) \( 12 q + q^{4} - 2 q^{7} + 2 q^{13} + q^{16} + 2 q^{19} + q^{25} + q^{28} - q^{31} + 13 q^{37} + 2 q^{43} - 2 q^{49} - 8 q^{52} - 8 q^{61} - 2 q^{64} - q^{67} + 2 q^{73} - 4 q^{76} - q^{79} + 2 q^{91} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1323.1.br.a 1323.br 147.n $12$ $0.660$ \(\Q(\zeta_{21})\) $D_{21}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{42}^{13}q^{4}-\zeta_{42}^{3}q^{7}+(-\zeta_{42}-\zeta_{42}^{5}+\cdots)q^{13}+\cdots\)