Properties

Label 3724.1.bk
Level $3724$
Weight $1$
Character orbit 3724.bk
Rep. character $\chi_{3724}(1451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $560$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3724.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 532 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(560\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 44 20 24
Cusp forms 12 4 8
Eisenstein series 32 16 16

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

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

Trace form

\( 4q - 4q^{4} - 2q^{6} + O(q^{10}) \) \( 4q - 4q^{4} - 2q^{6} - 2q^{13} + 4q^{16} - 2q^{17} - 2q^{22} + 2q^{24} - 4q^{25} - 2q^{29} - 4q^{33} - 2q^{37} - 4q^{38} + 2q^{41} + 2q^{46} + 2q^{52} + 4q^{54} - 2q^{57} + 2q^{61} - 2q^{62} - 4q^{64} + 2q^{68} + 4q^{69} - 2q^{73} - 2q^{78} + 2q^{81} + 2q^{86} + 2q^{88} - 2q^{89} - 4q^{93} + 2q^{94} - 2q^{96} - 2q^{97} + O(q^{100}) \)

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.bk.a \(4\) \(1.859\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{4}q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3724, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3724, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)