Properties

Label 1323.1.d
Level $1323$
Weight $1$
Character orbit 1323.d
Rep. character $\chi_{1323}(244,\cdot)$
Character field $\Q$
Dimension $2$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
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 30 2 28
Cusp forms 6 2 4
Eisenstein series 24 0 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q - 2 q^{4} + O(q^{10}) \) \( 2 q - 2 q^{4} + 2 q^{16} + 2 q^{25} + 2 q^{37} + 2 q^{43} - 2 q^{64} - 2 q^{67} - 2 q^{79} + O(q^{100}) \)

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.d.a 1323.d 7.b $2$ $0.660$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+q^{16}+q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)