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Properties

Label 3969.1.m
Level $3969$
Weight $1$
Character orbit 3969.m
Rep. character $\chi_{3969}(325,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $3$
Sturm bound $504$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 122 24 98
Cusp forms 26 8 18
Eisenstein series 96 16 80

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 4 q^{4} + O(q^{10}) \) \( 8 q - 4 q^{4} - 8 q^{22} - 4 q^{25} + 4 q^{46} + 4 q^{58} + 4 q^{67} + 4 q^{79} + 8 q^{88} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3969.1.m.a 3969.m 7.d $2$ $1.981$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-q^{8}-\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.m.b 3969.m 7.d $2$ $1.981$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+q^{8}+\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.m.c 3969.m 7.d $4$ $1.981$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3969, [\chi]) \cong \)