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

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

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3724.1.bb.a \(4\) \(1.859\) \(\Q(\zeta_{12})\) \(A_{4}\) 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 \(4\) \(1.859\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)