Properties

Label 15.3.d
Level 15
Weight 3
Character orbit d
Rep. character \(\chi_{15}(14,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 2
Sturm bound 6
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 15.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(15, [\chi])\).

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

Trace form

\( 2q - 6q^{4} - 6q^{6} + 18q^{9} + O(q^{10}) \) \( 2q - 6q^{4} - 6q^{6} + 18q^{9} + 10q^{10} - 30q^{15} + 10q^{16} - 44q^{19} + 42q^{24} + 50q^{25} + 4q^{31} - 28q^{34} - 54q^{36} - 70q^{40} + 68q^{46} + 98q^{49} + 84q^{51} - 54q^{54} + 90q^{60} - 236q^{61} + 26q^{64} - 204q^{69} + 132q^{76} + 196q^{79} + 162q^{81} - 140q^{85} + 90q^{90} - 28q^{94} - 198q^{96} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.3.d.a \(1\) \(0.409\) \(\Q\) \(\Q(\sqrt{-15}) \) \(-1\) \(3\) \(-5\) \(0\) \(q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots\)
15.3.d.b \(1\) \(0.409\) \(\Q\) \(\Q(\sqrt{-15}) \) \(1\) \(-3\) \(5\) \(0\) \(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 4 T^{2} \))(\( 1 - T + 4 T^{2} \))
$3$ (\( 1 - 3 T \))(\( 1 + 3 T \))
$5$ (\( 1 + 5 T \))(\( 1 - 5 T \))
$7$ (\( ( 1 - 7 T )( 1 + 7 T ) \))(\( ( 1 - 7 T )( 1 + 7 T ) \))
$11$ (\( ( 1 - 11 T )( 1 + 11 T ) \))(\( ( 1 - 11 T )( 1 + 11 T ) \))
$13$ (\( ( 1 - 13 T )( 1 + 13 T ) \))(\( ( 1 - 13 T )( 1 + 13 T ) \))
$17$ (\( 1 - 14 T + 289 T^{2} \))(\( 1 + 14 T + 289 T^{2} \))
$19$ (\( 1 + 22 T + 361 T^{2} \))(\( 1 + 22 T + 361 T^{2} \))
$23$ (\( 1 + 34 T + 529 T^{2} \))(\( 1 - 34 T + 529 T^{2} \))
$29$ (\( ( 1 - 29 T )( 1 + 29 T ) \))(\( ( 1 - 29 T )( 1 + 29 T ) \))
$31$ (\( 1 - 2 T + 961 T^{2} \))(\( 1 - 2 T + 961 T^{2} \))
$37$ (\( ( 1 - 37 T )( 1 + 37 T ) \))(\( ( 1 - 37 T )( 1 + 37 T ) \))
$41$ (\( ( 1 - 41 T )( 1 + 41 T ) \))(\( ( 1 - 41 T )( 1 + 41 T ) \))
$43$ (\( ( 1 - 43 T )( 1 + 43 T ) \))(\( ( 1 - 43 T )( 1 + 43 T ) \))
$47$ (\( 1 - 14 T + 2209 T^{2} \))(\( 1 + 14 T + 2209 T^{2} \))
$53$ (\( 1 - 86 T + 2809 T^{2} \))(\( 1 + 86 T + 2809 T^{2} \))
$59$ (\( ( 1 - 59 T )( 1 + 59 T ) \))(\( ( 1 - 59 T )( 1 + 59 T ) \))
$61$ (\( 1 + 118 T + 3721 T^{2} \))(\( 1 + 118 T + 3721 T^{2} \))
$67$ (\( ( 1 - 67 T )( 1 + 67 T ) \))(\( ( 1 - 67 T )( 1 + 67 T ) \))
$71$ (\( ( 1 - 71 T )( 1 + 71 T ) \))(\( ( 1 - 71 T )( 1 + 71 T ) \))
$73$ (\( ( 1 - 73 T )( 1 + 73 T ) \))(\( ( 1 - 73 T )( 1 + 73 T ) \))
$79$ (\( 1 - 98 T + 6241 T^{2} \))(\( 1 - 98 T + 6241 T^{2} \))
$83$ (\( 1 + 154 T + 6889 T^{2} \))(\( 1 - 154 T + 6889 T^{2} \))
$89$ (\( ( 1 - 89 T )( 1 + 89 T ) \))(\( ( 1 - 89 T )( 1 + 89 T ) \))
$97$ (\( ( 1 - 97 T )( 1 + 97 T ) \))(\( ( 1 - 97 T )( 1 + 97 T ) \))
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