Properties

Label 3969.1.l
Level $3969$
Weight $1$
Character orbit 3969.l
Rep. character $\chi_{3969}(1567,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $504$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3969.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(504\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3969, [\chi])\).

Total New Old
Modular forms 120 12 108
Cusp forms 24 4 20
Eisenstein series 96 8 88

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

\( 4 q + 2 q^{4} - 2 q^{16} - 2 q^{25} + 4 q^{37} - 2 q^{43} - 4 q^{64} + 2 q^{67} + 2 q^{79}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(3969, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3969.1.l.a 3969.l 63.l $2$ $1.981$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None 189.1.m.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.l.b 3969.l 63.l $2$ $1.981$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None 189.1.m.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3969, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3969, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)