Properties

Label 3724.1.bc
Level $3724$
Weight $1$
Character orbit 3724.bc
Rep. character $\chi_{3724}(569,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $4$
Sturm bound $560$
Trace bound $11$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3724.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(560\)
Trace bound: \(11\)

Dimensions

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

Total New Old
Modular forms 82 8 74
Cusp forms 34 8 26
Eisenstein series 48 0 48

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

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

Trace form

\( 8q + q^{5} - 4q^{9} + O(q^{10}) \) \( 8q + q^{5} - 4q^{9} + q^{11} - 2q^{17} + 2q^{19} - 2q^{23} - 3q^{25} - 2q^{43} + q^{45} + q^{47} + 8q^{55} + q^{61} + q^{73} - 4q^{81} + 4q^{83} + 2q^{85} + q^{95} - 2q^{99} + O(q^{100}) \)

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.bc.a \(2\) \(1.859\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots\)
3724.1.bc.b \(2\) \(1.859\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots\)
3724.1.bc.c \(2\) \(1.859\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}^{2}q^{17}+\cdots\)
3724.1.bc.d \(2\) \(1.859\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3724, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(931, [\chi])\)\(^{\oplus 3}\)