Properties

Label 3724.1.bb
Level $3724$
Weight $1$
Character orbit 3724.bb
Rep. character $\chi_{3724}(2059,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $560$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3724.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(560\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3724, [\chi])\).

Total New Old
Modular forms 40 28 12
Cusp forms 8 8 0
Eisenstein series 32 20 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 8 0 0

Trace form

\( 8 q + 4 q^{4} + O(q^{10}) \) \( 8 q + 4 q^{4} - 4 q^{16} - 4 q^{22} + 4 q^{25} - 4 q^{29} + 8 q^{37} - 8 q^{46} - 4 q^{57} - 8 q^{64} - 4 q^{78} + 4 q^{81} + 4 q^{86} - 8 q^{88} + 4 q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3724, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3724.1.bb.a 3724.bb 76.g $4$ $1.859$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
3724.1.bb.b 3724.bb 76.g $4$ $1.859$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)