Properties

Label 19.2.a
Level 19
Weight 2
Character orbit 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.

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

Trace form

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 19
19.2.a.a \(1\) \(0.152\) \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) \(-\) \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} \)
$3$ \( 1 + 2 T + 3 T^{2} \)
$5$ \( 1 - 3 T + 5 T^{2} \)
$7$ \( 1 + T + 7 T^{2} \)
$11$ \( 1 - 3 T + 11 T^{2} \)
$13$ \( 1 + 4 T + 13 T^{2} \)
$17$ \( 1 + 3 T + 17 T^{2} \)
$19$ \( 1 - T \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 - 6 T + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 - 2 T + 37 T^{2} \)
$41$ \( 1 + 6 T + 41 T^{2} \)
$43$ \( 1 + T + 43 T^{2} \)
$47$ \( 1 + 3 T + 47 T^{2} \)
$53$ \( 1 - 12 T + 53 T^{2} \)
$59$ \( 1 + 6 T + 59 T^{2} \)
$61$ \( 1 + T + 61 T^{2} \)
$67$ \( 1 + 4 T + 67 T^{2} \)
$71$ \( 1 - 6 T + 71 T^{2} \)
$73$ \( 1 + 7 T + 73 T^{2} \)
$79$ \( 1 - 8 T + 79 T^{2} \)
$83$ \( 1 - 12 T + 83 T^{2} \)
$89$ \( 1 - 12 T + 89 T^{2} \)
$97$ \( 1 - 8 T + 97 T^{2} \)
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