Properties

Label 19.3.b
Level 19
Weight 3
Character orbit b
Rep. character \(\chi_{19}(18,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 2
Sturm bound 5
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 19.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(19, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3q - 14q^{4} - q^{5} + 26q^{6} - 15q^{7} + q^{9} + O(q^{10}) \) \( 3q - 14q^{4} - q^{5} + 26q^{6} - 15q^{7} + q^{9} - 17q^{11} + 74q^{16} + 45q^{17} - 31q^{19} - 108q^{20} + 40q^{23} - 130q^{24} + 38q^{25} - 26q^{26} + 70q^{28} + 104q^{30} + 5q^{35} + 108q^{36} - 130q^{38} + 26q^{39} - 130q^{42} - 125q^{43} + 192q^{44} - 113q^{45} + 95q^{47} - 72q^{49} + 130q^{54} - 107q^{55} + 130q^{57} - 130q^{58} + 23q^{61} + 260q^{62} - 5q^{63} + 62q^{64} - 260q^{66} - 210q^{68} + 185q^{73} + 156q^{74} + 32q^{76} + 85q^{77} + 88q^{80} - 121q^{81} - 260q^{82} + 10q^{83} - 15q^{85} + 130q^{87} - 750q^{92} - 260q^{93} + 123q^{95} + 234q^{96} + 107q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.3.b.a \(1\) \(0.518\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-9\) \(-5\) \(q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots\)
19.3.b.b \(2\) \(0.518\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(8\) \(-10\) \(q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T )( 1 + 2 T ) \))(\( 1 + 5 T^{2} + 16 T^{4} \))
$3$ (\( ( 1 - 3 T )( 1 + 3 T ) \))(\( 1 - 5 T^{2} + 81 T^{4} \))
$5$ (\( 1 + 9 T + 25 T^{2} \))(\( ( 1 - 4 T + 25 T^{2} )^{2} \))
$7$ (\( 1 + 5 T + 49 T^{2} \))(\( ( 1 + 5 T + 49 T^{2} )^{2} \))
$11$ (\( 1 - 3 T + 121 T^{2} \))(\( ( 1 + 10 T + 121 T^{2} )^{2} \))
$13$ (\( ( 1 - 13 T )( 1 + 13 T ) \))(\( 1 - 325 T^{2} + 28561 T^{4} \))
$17$ (\( 1 - 15 T + 289 T^{2} \))(\( ( 1 - 15 T + 289 T^{2} )^{2} \))
$19$ (\( 1 + 19 T \))(\( 1 + 12 T + 361 T^{2} \))
$23$ (\( 1 + 30 T + 529 T^{2} \))(\( ( 1 - 35 T + 529 T^{2} )^{2} \))
$29$ (\( ( 1 - 29 T )( 1 + 29 T ) \))(\( 1 - 1357 T^{2} + 707281 T^{4} \))
$31$ (\( ( 1 - 31 T )( 1 + 31 T ) \))(\( 1 - 622 T^{2} + 923521 T^{4} \))
$37$ (\( ( 1 - 37 T )( 1 + 37 T ) \))(\( 1 - 2270 T^{2} + 1874161 T^{4} \))
$41$ (\( ( 1 - 41 T )( 1 + 41 T ) \))(\( 1 - 2062 T^{2} + 2825761 T^{4} \))
$43$ (\( 1 + 85 T + 1849 T^{2} \))(\( ( 1 + 20 T + 1849 T^{2} )^{2} \))
$47$ (\( 1 - 75 T + 2209 T^{2} \))(\( ( 1 - 10 T + 2209 T^{2} )^{2} \))
$53$ (\( ( 1 - 53 T )( 1 + 53 T ) \))(\( 1 + 115 T^{2} + 7890481 T^{4} \))
$59$ (\( ( 1 - 59 T )( 1 + 59 T ) \))(\( 1 - 6637 T^{2} + 12117361 T^{4} \))
$61$ (\( 1 - 103 T + 3721 T^{2} \))(\( ( 1 + 40 T + 3721 T^{2} )^{2} \))
$67$ (\( ( 1 - 67 T )( 1 + 67 T ) \))(\( 1 - 7405 T^{2} + 20151121 T^{4} \))
$71$ (\( ( 1 - 71 T )( 1 + 71 T ) \))(\( ( 1 - 92 T + 5041 T^{2} )( 1 + 92 T + 5041 T^{2} ) \))
$73$ (\( 1 + 25 T + 5329 T^{2} \))(\( ( 1 - 105 T + 5329 T^{2} )^{2} \))
$79$ (\( ( 1 - 79 T )( 1 + 79 T ) \))(\( 1 - 11182 T^{2} + 38950081 T^{4} \))
$83$ (\( 1 - 90 T + 6889 T^{2} \))(\( ( 1 + 40 T + 6889 T^{2} )^{2} \))
$89$ (\( ( 1 - 89 T )( 1 + 89 T ) \))(\( ( 1 - 89 T )^{2}( 1 + 89 T )^{2} \))
$97$ (\( ( 1 - 97 T )( 1 + 97 T ) \))(\( 1 - 3790 T^{2} + 88529281 T^{4} \))
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