Properties

Label 15.2.a
Level 15
Weight 2
Character orbit a
Rep. character \(\chi_{15}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\) into irreducible Hecke orbits

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 \(-1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)