Properties

Label 15.3.d
Level 15
Weight 3
Character orbit d
Rep. character \(\chi_{15}(14,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(15, [\chi])\) into irreducible Hecke orbits

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 \(1\) \(0.409\) \(\Q\) \(\Q(\sqrt{-15}) \) \(1\) \(-3\) \(5\) \(0\) \(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)