Properties

Label 1007.1.d
Level $1007$
Weight $1$
Character orbit 1007.d
Rep. character $\chi_{1007}(1006,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $6$
Sturm bound $90$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1007 = 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1007.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1007 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(90\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1007, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 14 14 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14 q + 12 q^{4} - 4 q^{6} - 2 q^{7} + 12 q^{9} + O(q^{10}) \) \( 14 q + 12 q^{4} - 4 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{11} + 10 q^{16} - 2 q^{17} - 8 q^{24} + 14 q^{25} - 6 q^{28} + 6 q^{36} - 2 q^{38} - 8 q^{42} - 2 q^{43} - 6 q^{44} - 2 q^{47} + 12 q^{49} - 8 q^{54} - 2 q^{57} - 4 q^{62} - 6 q^{63} + 8 q^{64} - 8 q^{66} - 6 q^{68} - 4 q^{77} + 10 q^{81} - 4 q^{82} - 4 q^{93} - 12 q^{96} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1007, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1007.1.d.a 1007.d 1007.d $1$ $0.503$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1007}) \) None \(-1\) \(-1\) \(0\) \(2\) \(q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}-q^{11}+\cdots\)
1007.1.d.b 1007.d 1007.d $1$ $0.503$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1007}) \) None \(1\) \(1\) \(0\) \(2\) \(q+q^{2}+q^{3}+q^{6}+2q^{7}-q^{8}-q^{11}+\cdots\)
1007.1.d.c 1007.d 1007.d $2$ $0.503$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-1007}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1007.1.d.d 1007.d 1007.d $2$ $0.503$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-1007}) \) None \(1\) \(1\) \(0\) \(-1\) \(q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1007.1.d.e 1007.d 1007.d $4$ $0.503$ \(\Q(\zeta_{15})^+\) $D_{15}$ \(\Q(\sqrt{-1007}) \) None \(-1\) \(-1\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1007.1.d.f 1007.d 1007.d $4$ $0.503$ \(\Q(\zeta_{15})^+\) $D_{15}$ \(\Q(\sqrt{-1007}) \) None \(1\) \(1\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)