Properties

Label 3969.1.r
Level $3969$
Weight $1$
Character orbit 3969.r
Rep. character $\chi_{3969}(1079,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $4$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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 112 26 86
Cusp forms 16 16 0
Eisenstein series 96 10 86

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q + 4q^{4} + O(q^{10}) \) \( 16q + 4q^{4} - 8q^{16} - 8q^{25} - 4q^{37} + 2q^{43} - 8q^{64} + 2q^{67} + 2q^{79} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3969.1.r.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}-q^{19}+\cdots\)
3969.1.r.b \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+q^{19}+\cdots\)
3969.1.r.c \(4\) \(1.981\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(D_{4}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
3969.1.r.d \(8\) \(1.981\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)