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 $0$

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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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5
15.2.a.a 15.a 1.a $1$ $0.120$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)