Properties

Label 19.2.a
Level $19$
Weight $2$
Character orbit 19.a
Rep. character $\chi_{19}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 19.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(19))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(19\)Dim
\(-\)\(1\)

Trace form

\( q - 2 q^{3} - 2 q^{4} + 3 q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( q - 2 q^{3} - 2 q^{4} + 3 q^{5} - q^{7} + q^{9} + 3 q^{11} + 4 q^{12} - 4 q^{13} - 6 q^{15} + 4 q^{16} - 3 q^{17} + q^{19} - 6 q^{20} + 2 q^{21} + 4 q^{25} + 4 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{31} - 6 q^{33} - 3 q^{35} - 2 q^{36} + 2 q^{37} + 8 q^{39} - 6 q^{41} - q^{43} - 6 q^{44} + 3 q^{45} - 3 q^{47} - 8 q^{48} - 6 q^{49} + 6 q^{51} + 8 q^{52} + 12 q^{53} + 9 q^{55} - 2 q^{57} - 6 q^{59} + 12 q^{60} - q^{61} - q^{63} - 8 q^{64} - 12 q^{65} - 4 q^{67} + 6 q^{68} + 6 q^{71} - 7 q^{73} - 8 q^{75} - 2 q^{76} - 3 q^{77} + 8 q^{79} + 12 q^{80} - 11 q^{81} + 12 q^{83} - 4 q^{84} - 9 q^{85} - 12 q^{87} + 12 q^{89} + 4 q^{91} + 8 q^{93} + 3 q^{95} + 8 q^{97} + 3 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 19
19.2.a.a 19.a 1.a $1$ $0.152$ \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)