Properties

Label 15.3.d
Level $15$
Weight $3$
Character orbit 15.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 \(1\) \(0.409\) \(\Q\) \(\Q(\sqrt{-15}) \) \(1\) \(-3\) \(5\) \(0\) \(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)