↑

Properties

Label 1045.1.w
Level $1045$
Weight $1$
Character orbit 1045.w
Rep. character $\chi_{1045}(284,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $40$
Newform subspaces $6$
Sturm bound $120$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1045.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 6 \)
Sturm bound: \(120\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1045, [\chi])\).

Total New Old
Modular forms 56 56 0
Cusp forms 40 40 0
Eisenstein series 16 16 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 0 0 0

Trace form

\( 40 q - 6 q^{4} - 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 40 q - 6 q^{4} - 2 q^{5} - 6 q^{9} + 2 q^{11} - 10 q^{16} - 2 q^{19} + 2 q^{20} - 16 q^{24} - 10 q^{25} - 16 q^{26} - 16 q^{30} - 5 q^{35} + 14 q^{36} + 2 q^{45} + 64 q^{54} - 3 q^{55} - 6 q^{61} - 6 q^{64} - 8 q^{66} - 8 q^{76} + 27 q^{80} - 10 q^{81} - 5 q^{85} - 5 q^{95} + 8 q^{96} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1045.1.w.a 1045.w 1045.w $4$ $0.522$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-95}) \) None \(-2\) \(-2\) \(-1\) \(0\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
1045.1.w.b 1045.w 1045.w $4$ $0.522$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-5\) \(q+\zeta_{10}q^{4}-\zeta_{10}q^{5}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1045.1.w.c 1045.w 1045.w $4$ $0.522$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(5\) \(q+\zeta_{10}q^{4}-\zeta_{10}^{3}q^{5}+(1-\zeta_{10}^{2})q^{7}+\cdots\)
1045.1.w.d 1045.w 1045.w $4$ $0.522$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-95}) \) None \(2\) \(2\) \(-1\) \(0\) \(q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
1045.1.w.e 1045.w 1045.w $8$ $0.522$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{3}+\cdots\)
1045.1.w.f 1045.w 1045.w $16$ $0.522$ \(\Q(\zeta_{40})\) $D_{20}$ \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{11}+\zeta_{40}^{13}+\cdots)q^{3}+\cdots\)