Properties

Label 3724.1.dj
Level $3724$
Weight $1$
Character orbit 3724.dj
Rep. character $\chi_{3724}(37,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $24$
Newform subspaces $2$
Sturm bound $560$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3724.dj (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 931 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 2 \)
Sturm bound: \(560\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 132 24 108
Cusp forms 60 24 36
Eisenstein series 72 0 72

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24q + q^{5} - q^{7} + 2q^{9} + O(q^{10}) \) \( 24q + q^{5} - q^{7} + 2q^{9} + 8q^{11} + 5q^{17} - 12q^{19} - 2q^{23} + 3q^{25} - 5q^{35} - 2q^{43} - 13q^{45} + q^{47} - q^{49} - 6q^{55} + q^{61} - q^{63} + q^{73} + q^{77} + 2q^{81} + 4q^{83} + 2q^{85} + q^{95} - 2q^{99} + O(q^{100}) \)

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.dj.a \(12\) \(1.859\) \(\Q(\zeta_{21})\) \(D_{21}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q+(-\zeta_{42}-\zeta_{42}^{3})q^{5}-\zeta_{42}^{9}q^{7}-\zeta_{42}^{11}q^{9}+\cdots\)
3724.1.dj.b \(12\) \(1.859\) \(\Q(\zeta_{21})\) \(D_{21}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(1\) \(q+(\zeta_{42}^{8}-\zeta_{42}^{17})q^{5}+\zeta_{42}^{16}q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3724, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(931, [\chi])\)\(^{\oplus 3}\)