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Properties

Label 1005.1.p
Level $1005$
Weight $1$
Character orbit 1005.p
Rep. character $\chi_{1005}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $136$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1005 = 3 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1005.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1005 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(136\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1005, [\chi])\).

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 0 8 0 0

Trace form

\( 8 q - 8 q^{9} + O(q^{10}) \) \( 8 q - 8 q^{9} + 4 q^{16} - 4 q^{19} - 4 q^{21} - 8 q^{25} - 4 q^{30} + 4 q^{31} + 4 q^{34} + 4 q^{39} - 4 q^{46} + 4 q^{55} + 4 q^{61} + 8 q^{64} + 8 q^{66} - 8 q^{70} - 4 q^{79} + 8 q^{81} + 8 q^{91} - 8 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1005, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1005.1.p.a 1005.p 1005.p $4$ $0.502$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{3}q^{5}+\cdots\)
1005.1.p.b 1005.p 1005.p $4$ $0.502$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)