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Properties

Label 3751.1.t
Level $3751$
Weight $1$
Character orbit 3751.t
Rep. character $\chi_{3751}(2138,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $68$
Newform subspaces $7$
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.t (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 341 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 7 \)
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 116 100 16
Cusp forms 68 68 0
Eisenstein series 48 32 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 68 0 0 0

Trace form

\( 68 q - 15 q^{4} + 2 q^{5} - 17 q^{9} + O(q^{10}) \) \( 68 q - 15 q^{4} + 2 q^{5} - 17 q^{9} + 4 q^{14} - 13 q^{16} + 6 q^{20} - 15 q^{25} + q^{31} - 15 q^{36} + 4 q^{38} - 8 q^{45} + 2 q^{47} - 15 q^{49} - 32 q^{56} + 2 q^{59} - 11 q^{64} - 8 q^{67} + 8 q^{70} + 2 q^{71} + 10 q^{80} - 17 q^{81} + 4 q^{82} + 2 q^{97} + O(q^{100}) \)

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.t.a 3751.t 341.t $4$ $1.872$ \(\Q(\zeta_{10})\) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{2}q^{5}-\zeta_{10}q^{7}-\zeta_{10}^{4}q^{8}+\cdots\)
3751.1.t.b 3751.t 341.t $4$ $1.872$ \(\Q(\zeta_{10})\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-31}) \) \(\Q(\sqrt{341}) \) \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{10}q^{4}+\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+\zeta_{10}^{2}q^{16}+\cdots\)
3751.1.t.c 3751.t 341.t $4$ $1.872$ \(\Q(\zeta_{10})\) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(1\) \(0\) \(1\) \(1\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{2}q^{5}+\zeta_{10}q^{7}+\zeta_{10}^{4}q^{8}+\cdots\)
3751.1.t.d 3751.t 341.t $8$ $1.872$ 8.0.324000000.3 $D_{6}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{7}q^{2}+2\beta _{4}q^{4}+(1+\beta _{2}+\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots\)
3751.1.t.e 3751.t 341.t $12$ $1.872$ 12.0.\(\cdots\).1 $D_{9}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(\beta _{6}+\beta _{7}-\beta _{8})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
3751.1.t.f 3751.t 341.t $12$ $1.872$ 12.0.\(\cdots\).1 $D_{9}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(\beta _{6}+\beta _{7}-\beta _{8})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
3751.1.t.g 3751.t 341.t $24$ $1.872$ 24.0.\(\cdots\).2 $D_{18}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{9}+\beta _{11}-\beta _{14}+\beta _{17}+\cdots)q^{2}+\cdots\)