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Properties

Label 3751.1.d
Level $3751$
Weight $1$
Character orbit 3751.d
Rep. character $\chi_{3751}(1332,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $6$
Sturm bound $352$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 3751 = 11^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3751.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(352\)
Trace bound: \(8\)

Dimensions

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

Total New Old
Modular forms 31 25 6
Cusp forms 19 16 3
Eisenstein series 12 9 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q + q^{2} + 15 q^{4} - q^{5} + q^{7} - q^{8} + 16 q^{9} + O(q^{10}) \) \( 16 q + q^{2} + 15 q^{4} - q^{5} + q^{7} - q^{8} + 16 q^{9} - q^{10} - 5 q^{14} + 14 q^{16} + q^{18} + q^{19} - 6 q^{20} + 15 q^{25} - 2 q^{31} - q^{35} + 15 q^{36} - 5 q^{38} + q^{40} + q^{41} - q^{45} - 4 q^{47} + 15 q^{49} - 7 q^{56} - q^{59} + q^{62} + q^{63} + 10 q^{64} - 4 q^{67} - 7 q^{70} - q^{71} - q^{72} - 11 q^{80} + 16 q^{81} - 5 q^{82} - q^{90} + 2 q^{94} - q^{95} - q^{97} + O(q^{100}) \)

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.d.a 3751.d 31.b $1$ $1.872$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-31}) \) \(\Q(\sqrt{341}) \) \(0\) \(0\) \(2\) \(0\) \(q-q^{4}+2q^{5}+q^{9}+q^{16}-2q^{20}+\cdots\)
3751.1.d.b 3751.d 31.b $1$ $1.872$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+q^{2}-q^{5}+q^{7}-q^{8}+q^{9}-q^{10}+\cdots\)
3751.1.d.c 3751.d 31.b $2$ $1.872$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+2q^{4}-q^{5}-\beta q^{7}-\beta q^{8}+\cdots\)
3751.1.d.d 3751.d 31.b $3$ $1.872$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
3751.1.d.e 3751.d 31.b $3$ $1.872$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
3751.1.d.f 3751.d 31.b $6$ $1.872$ \(\Q(\zeta_{36})^+\) $D_{18}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3751, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(341, [\chi])\)\(^{\oplus 2}\)