Properties

Label 3969.1.b
Level $3969$
Weight $1$
Character orbit 3969.b
Rep. character $\chi_{3969}(3725,\cdot)$
Character field $\Q$
Dimension $4$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
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 62 14 48
Cusp forms 14 4 10
Eisenstein series 48 10 38

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - 4 q^{4} + O(q^{10}) \) \( 4 q - 4 q^{4} + 8 q^{16} + 4 q^{22} + 4 q^{25} - 4 q^{46} - 4 q^{58} - 8 q^{64} + 4 q^{67} - 4 q^{79} + O(q^{100}) \)

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.b.a $4$ $1.981$ \(\Q(\sqrt{-2}, \sqrt{3})\) $D_{12}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(2\beta _{1}-\beta _{3})q^{8}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)