Properties

Label 3751.1.bu
Level $3751$
Weight $1$
Character orbit 3751.bu
Rep. character $\chi_{3751}(487,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8$
Newform subspaces $1$
Sturm bound $352$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3751 = 11^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3751.bu (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 341 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(352\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3751, [\chi])\).

Total New Old
Modular forms 104 72 32
Cusp forms 8 8 0
Eisenstein series 96 64 32

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

\( 8 q - 5 q^{3} + 2 q^{4} - q^{5} - 4 q^{9} + O(q^{10}) \) \( 8 q - 5 q^{3} + 2 q^{4} - q^{5} - 4 q^{9} - 2 q^{16} + q^{20} - 5 q^{23} + 10 q^{27} - q^{31} + 4 q^{36} - 3 q^{37} - 6 q^{45} - 2 q^{47} - q^{49} - 2 q^{53} - q^{59} - 5 q^{60} + 2 q^{64} - q^{67} - 5 q^{69} - 4 q^{71} + 5 q^{75} - q^{80} - 4 q^{81} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3751, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3751.1.bu.a 3751.bu 341.aq $8$ $1.872$ \(\Q(\zeta_{15})\) $D_{30}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-5\) \(-1\) \(0\) \(q+(\zeta_{30}^{10}+\zeta_{30}^{13})q^{3}+\zeta_{30}^{9}q^{4}+\cdots\)