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Properties

Label 1045.1.br
Level $1045$
Weight $1$
Character orbit 1045.br
Rep. character $\chi_{1045}(18,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $16$
Newform subspaces $2$
Sturm bound $120$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1045.br (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
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 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

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

\( 16 q - 4 q^{5} - 10 q^{7} + O(q^{10}) \) \( 16 q - 4 q^{5} - 10 q^{7} + 4 q^{16} - 10 q^{17} + 4 q^{23} - 4 q^{25} + 4 q^{36} - 4 q^{47} + 10 q^{63} + 10 q^{68} - 4 q^{77} - 6 q^{80} + 4 q^{81} - 4 q^{92} - 10 q^{95} + O(q^{100}) \)

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.br.a 1045.br 1045.ar $8$ $0.522$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-8\) \(q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{4}q^{5}+(-1-\zeta_{20}+\cdots)q^{7}+\cdots\)
1045.1.br.b 1045.br 1045.ar $8$ $0.522$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-2\) \(q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{5}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots\)