Properties

Label 3969.1.j
Level $3969$
Weight $1$
Character orbit 3969.j
Rep. character $\chi_{3969}(863,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
Newform subspaces $3$
Sturm bound $504$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 114 22 92
Cusp forms 18 14 4
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 14 0 0 0

Trace form

\( 14q - 10q^{4} + O(q^{10}) \) \( 14q - 10q^{4} - q^{13} + 14q^{16} + 2q^{19} - 7q^{25} + 2q^{31} + q^{37} + q^{43} - q^{52} + 2q^{61} - 10q^{64} - 2q^{67} + 2q^{73} + 2q^{76} - 2q^{79} - q^{97} + O(q^{100}) \)

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.j.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-\zeta_{6}q^{13}+q^{16}+\zeta_{6}q^{19}-\zeta_{6}q^{25}+\cdots\)
3969.1.j.b \(4\) \(1.981\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(D_{4}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-q^{4}+(-\beta _{1}+\beta _{3})q^{11}-q^{16}+\cdots\)
3969.1.j.c \(8\) \(1.981\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}+\zeta_{24}^{11})q^{2}+(-1+\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)

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

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