Properties

Label 3744.1.ck
Level $3744$
Weight $1$
Character orbit 3744.ck
Rep. character $\chi_{3744}(607,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $672$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3744.ck (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 468 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(672\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3744, [\chi])\).

Total New Old
Modular forms 52 4 48
Cusp forms 20 4 16
Eisenstein series 32 0 32

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

\( 4q + 2q^{5} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{5} + 2q^{9} + 2q^{13} - 2q^{17} + 4q^{29} - 2q^{33} - 2q^{37} - 2q^{45} - 2q^{49} - 2q^{57} + 4q^{65} + 8q^{73} - 2q^{81} - 4q^{85} - 2q^{89} + 4q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3744.1.ck.a \(4\) \(1.868\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{5}-\zeta_{12}^{4}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 4}\)