Properties

Label 3744.1.bv
Level $3744$
Weight $1$
Character orbit 3744.bv
Rep. character $\chi_{3744}(737,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $672$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3744.bv (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
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 136 8 128
Cusp forms 72 8 64
Eisenstein series 64 0 64

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

\( 8q + O(q^{10}) \) \( 8q - 8q^{25} - 4q^{37} + 4q^{49} + 4q^{61} - 8q^{85} + O(q^{100}) \)

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.bv.a \(8\) \(1.868\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}+\zeta_{24}^{11})q^{5}+\zeta_{24}^{2}q^{13}+(-\zeta_{24}^{3}+\cdots)q^{17}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1872, [\chi])\)\(^{\oplus 2}\)