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Properties

Label 1045.1.k
Level $1045$
Weight $1$
Character orbit 1045.k
Rep. character $\chi_{1045}(208,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $4$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
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 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 4 q^{5} + O(q^{10}) \) \( 8 q + 4 q^{5} + 4 q^{11} + 4 q^{20} - 8 q^{23} - 8 q^{26} + 4 q^{38} - 4 q^{45} - 8 q^{58} + 4 q^{77} - 4 q^{80} - 8 q^{81} + O(q^{100}) \)

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.k.a 1045.k 1045.k $2$ $0.522$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{209}) \) \(-2\) \(0\) \(0\) \(0\) \(q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\cdots\)
1045.1.k.b 1045.k 1045.k $2$ $0.522$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(-2\) \(q-iq^{4}+q^{5}+(-1+i)q^{7}-iq^{9}+\cdots\)
1045.1.k.c 1045.k 1045.k $2$ $0.522$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(2\) \(q-iq^{4}+q^{5}+(1-i)q^{7}-iq^{9}+iq^{11}+\cdots\)
1045.1.k.d 1045.k 1045.k $2$ $0.522$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{209}) \) \(2\) \(0\) \(0\) \(0\) \(q+(1+i)q^{2}+iq^{4}-iq^{5}+q^{8}-iq^{9}+\cdots\)