Properties

Label 3969.1.k
Level $3969$
Weight $1$
Character orbit 3969.k
Rep. character $\chi_{3969}(460,\cdot)$
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.k (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

\( 12q - 2q^{4} + O(q^{10}) \) \( 12q - 2q^{4} + 3q^{13} - 2q^{16} + 4q^{22} + 12q^{25} - 3q^{31} + q^{37} + q^{43} + 4q^{46} - 8q^{58} + 3q^{61} - 4q^{64} + 3q^{67} + 3q^{79} - 16q^{88} + 3q^{97} + O(q^{100}) \)

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

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