Properties

Label 3724.1.bv
Level $3724$
Weight $1$
Character orbit 3724.bv
Rep. character $\chi_{3724}(113,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $12$
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.bv (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 931 \)
Character field: \(\Q(\zeta_{14})\)
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 66 12 54
Cusp forms 30 12 18
Eisenstein series 36 0 36

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

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

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.bv.a \(12\) \(1.859\) \(\Q(\zeta_{21})\) \(D_{21}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(1\) \(q+(-\zeta_{42}-\zeta_{42}^{5})q^{5}-\zeta_{42}^{17}q^{7}+\cdots\)

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

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