Properties

Label 3969.1.t
Level $3969$
Weight $1$
Character orbit 3969.t
Rep. character $\chi_{3969}(2971,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $5$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
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 20 92
Cusp forms 16 12 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 12 0 0 0

Trace form

\( 12q + 4q^{4} + O(q^{10}) \) \( 12q + 4q^{4} - 3q^{13} + 4q^{16} + 4q^{22} - 6q^{25} + q^{37} + q^{43} + 4q^{46} + 3q^{52} + 4q^{58} - 4q^{64} - 6q^{67} - 6q^{79} + 8q^{88} - 3q^{97} + O(q^{100}) \)

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.t.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{8}-\zeta_{6}^{2}q^{11}-q^{16}+\zeta_{6}^{2}q^{22}+\cdots\)
3969.1.t.b \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+(-1-\zeta_{6})q^{13}+q^{16}+\zeta_{6}^{2}q^{25}+\cdots\)
3969.1.t.c \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+q^{16}+\zeta_{6}^{2}q^{25}-\zeta_{6}^{2}q^{37}+\cdots\)
3969.1.t.d \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{8}+\zeta_{6}^{2}q^{11}-q^{16}+\zeta_{6}^{2}q^{22}+\cdots\)
3969.1.t.e \(4\) \(1.981\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{5})q^{2}+(1+\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)

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

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