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Properties

Label 1023.1.dk
Level $1023$
Weight $1$
Character orbit 1023.dk
Rep. character $\chi_{1023}(65,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $16$
Newform subspaces $2$
Sturm bound $128$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1023 = 3 \cdot 11 \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1023.dk (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1023 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1023, [\chi])\).

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

\( 16 q + 4 q^{4} + 2 q^{9} + O(q^{10}) \) \( 16 q + 4 q^{4} + 2 q^{9} - 5 q^{15} - 4 q^{16} + 6 q^{25} - 8 q^{31} - 4 q^{33} - 2 q^{36} - 24 q^{37} + 5 q^{45} + 5 q^{48} + 2 q^{49} - 6 q^{55} - 5 q^{60} + 4 q^{64} + 2 q^{67} + 2 q^{69} + 10 q^{75} + 2 q^{81} + 6 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1023, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1023.1.dk.a 1023.dk 1023.ck $8$ $0.511$ \(\Q(\zeta_{15})\) $D_{30}$ \(\Q(\sqrt{-11}) \) None 1023.1.dk.a \(0\) \(-1\) \(-3\) \(0\) \(q-\zeta_{30}^{14}q^{3}+\zeta_{30}^{3}q^{4}+(-\zeta_{30}^{9}+\cdots)q^{5}+\cdots\)
1023.1.dk.b 1023.dk 1023.ck $8$ $0.511$ \(\Q(\zeta_{15})\) $D_{30}$ \(\Q(\sqrt{-11}) \) None 1023.1.dk.a \(0\) \(1\) \(3\) \(0\) \(q+\zeta_{30}^{8}q^{3}+\zeta_{30}^{3}q^{4}+(\zeta_{30}^{9}-\zeta_{30}^{11}+\cdots)q^{5}+\cdots\)