Properties

Label 15.2.a
Level $15$
Weight $2$
Character orbit 15.a
Rep. character $\chi_{15}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 15.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(15))\).

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

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

\(3\)\(5\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} - 2q^{13} - q^{15} - q^{16} + 2q^{17} - q^{18} + 4q^{19} - q^{20} + 4q^{22} - 3q^{24} + q^{25} + 2q^{26} - q^{27} - 2q^{29} + q^{30} - 5q^{32} + 4q^{33} - 2q^{34} - q^{36} - 10q^{37} - 4q^{38} + 2q^{39} + 3q^{40} + 10q^{41} + 4q^{43} + 4q^{44} + q^{45} + 8q^{47} + q^{48} - 7q^{49} - q^{50} - 2q^{51} + 2q^{52} - 10q^{53} + q^{54} - 4q^{55} - 4q^{57} + 2q^{58} - 4q^{59} + q^{60} - 2q^{61} + 7q^{64} - 2q^{65} - 4q^{66} + 12q^{67} - 2q^{68} - 8q^{71} + 3q^{72} + 10q^{73} + 10q^{74} - q^{75} - 4q^{76} - 2q^{78} - q^{80} + q^{81} - 10q^{82} + 12q^{83} + 2q^{85} - 4q^{86} + 2q^{87} - 12q^{88} - 6q^{89} - q^{90} - 8q^{94} + 4q^{95} + 5q^{96} + 2q^{97} + 7q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5
15.2.a.a \(1\) \(0.120\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T + 2 T^{2} \)
$3$ \( 1 + T \)
$5$ \( 1 - T \)
$7$ \( 1 + 7 T^{2} \)
$11$ \( 1 + 4 T + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 - 2 T + 17 T^{2} \)
$19$ \( 1 - 4 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 + 2 T + 29 T^{2} \)
$31$ \( 1 + 31 T^{2} \)
$37$ \( 1 + 10 T + 37 T^{2} \)
$41$ \( 1 - 10 T + 41 T^{2} \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 - 8 T + 47 T^{2} \)
$53$ \( 1 + 10 T + 53 T^{2} \)
$59$ \( 1 + 4 T + 59 T^{2} \)
$61$ \( 1 + 2 T + 61 T^{2} \)
$67$ \( 1 - 12 T + 67 T^{2} \)
$71$ \( 1 + 8 T + 71 T^{2} \)
$73$ \( 1 - 10 T + 73 T^{2} \)
$79$ \( 1 + 79 T^{2} \)
$83$ \( 1 - 12 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 - 2 T + 97 T^{2} \)
show more
show less