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Properties

Label 3751.1.l
Level $3751$
Weight $1$
Character orbit 3751.l
Rep. character $\chi_{3751}(1451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $352$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3751 = 11^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3751.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 341 \)
Character field: \(\Q(\zeta_{6})\)
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 32 20 12
Cusp forms 8 4 4
Eisenstein series 24 16 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 4 0

Trace form

\( 4 q + 4 q^{4} - 2 q^{5} + 2 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{4} - 2 q^{5} + 2 q^{9} + 4 q^{16} - 2 q^{20} + 4 q^{23} - 2 q^{31} + 2 q^{36} + 2 q^{37} + 2 q^{45} - 4 q^{47} + 2 q^{49} - 2 q^{53} + 2 q^{59} + 4 q^{64} - 2 q^{67} + 2 q^{71} - 2 q^{80} - 2 q^{81} - 4 q^{89} + 4 q^{92} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.l.a 3751.l 341.l $4$ $1.872$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $S_{4}$ None None \(0\) \(0\) \(-2\) \(0\) \(q+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}+\beta _{2}q^{9}+q^{16}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3751, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3751, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(341, [\chi])\)\(^{\oplus 2}\)