Properties

Label 3969.1.bt
Level $3969$
Weight $1$
Character orbit 3969.bt
Rep. character $\chi_{3969}(134,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $12$
Newform subspaces $1$
Sturm bound $504$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3969.bt (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(504\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 156 36 120
Cusp forms 12 12 0
Eisenstein series 144 24 120

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

\( 12 q + q^{4} + q^{7} + O(q^{10}) \) \( 12 q + q^{4} + q^{7} + 2 q^{13} + q^{16} - 4 q^{19} + q^{25} - 2 q^{28} + 2 q^{31} + 10 q^{37} + 2 q^{43} + q^{49} - 5 q^{52} - 5 q^{61} - 2 q^{64} + 2 q^{67} - 4 q^{73} + 2 q^{76} + 2 q^{79} - 4 q^{91} + 2 q^{97} + O(q^{100}) \)

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.bt.a $12$ $1.981$ \(\Q(\zeta_{21})\) $D_{7}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{42}^{11}q^{4}+\zeta_{42}^{16}q^{7}+(\zeta_{42}^{8}-\zeta_{42}^{17}+\cdots)q^{13}+\cdots\)