Properties

Label 2019.1.g
Level $2019$
Weight $1$
Character orbit 2019.g
Rep. character $\chi_{2019}(731,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2019 = 3 \cdot 673 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2019.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2019 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2019, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q - 2 q^{3} - 2 q^{4} + 2 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{3} - 2 q^{4} + 2 q^{9} + 2 q^{12} - 4 q^{13} + 2 q^{16} + 2 q^{19} - 2 q^{27} - 2 q^{31} - 2 q^{36} + 4 q^{39} - 2 q^{43} - 2 q^{48} - 6 q^{49} + 4 q^{52} - 2 q^{57} - 2 q^{61} - 2 q^{64} - 2 q^{67} - 2 q^{76} + 2 q^{79} + 2 q^{81} + 2 q^{93} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2019, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2019.1.g.a 2019.g 2019.g $2$ $1.008$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-q^{4}-iq^{7}+q^{9}+q^{12}-q^{13}+\cdots\)