Properties

Label 15.5.d
Level 15
Weight 5
Character orbit d
Rep. character \(\chi_{15}(14,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 3
Sturm bound 10
Trace bound 2

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 15.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(10\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(15, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\(6q \) \(\mathstrut +\mathstrut 42q^{4} \) \(\mathstrut -\mathstrut 66q^{6} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 42q^{4} \) \(\mathstrut -\mathstrut 66q^{6} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut -\mathstrut 270q^{10} \) \(\mathstrut +\mathstrut 570q^{15} \) \(\mathstrut +\mathstrut 114q^{16} \) \(\mathstrut +\mathstrut 756q^{19} \) \(\mathstrut +\mathstrut 468q^{21} \) \(\mathstrut -\mathstrut 3462q^{24} \) \(\mathstrut -\mathstrut 930q^{25} \) \(\mathstrut +\mathstrut 2340q^{30} \) \(\mathstrut -\mathstrut 3708q^{31} \) \(\mathstrut +\mathstrut 8868q^{34} \) \(\mathstrut +\mathstrut 6210q^{36} \) \(\mathstrut -\mathstrut 7488q^{39} \) \(\mathstrut -\mathstrut 7710q^{40} \) \(\mathstrut +\mathstrut 7020q^{45} \) \(\mathstrut -\mathstrut 6612q^{46} \) \(\mathstrut +\mathstrut 13470q^{49} \) \(\mathstrut -\mathstrut 1596q^{51} \) \(\mathstrut -\mathstrut 19386q^{54} \) \(\mathstrut -\mathstrut 9360q^{55} \) \(\mathstrut +\mathstrut 14130q^{60} \) \(\mathstrut +\mathstrut 9252q^{61} \) \(\mathstrut +\mathstrut 10530q^{64} \) \(\mathstrut +\mathstrut 9360q^{66} \) \(\mathstrut -\mathstrut 6096q^{69} \) \(\mathstrut -\mathstrut 4680q^{70} \) \(\mathstrut +\mathstrut 9360q^{75} \) \(\mathstrut -\mathstrut 23100q^{76} \) \(\mathstrut -\mathstrut 5724q^{79} \) \(\mathstrut -\mathstrut 2754q^{81} \) \(\mathstrut -\mathstrut 2808q^{84} \) \(\mathstrut -\mathstrut 12060q^{85} \) \(\mathstrut -\mathstrut 31230q^{90} \) \(\mathstrut +\mathstrut 14976q^{91} \) \(\mathstrut +\mathstrut 28188q^{94} \) \(\mathstrut +\mathstrut 9522q^{96} \) \(\mathstrut +\mathstrut 28080q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.5.d.a \(1\) \(1.551\) \(\Q\) \(\Q(\sqrt{-15}) \) \(-7\) \(9\) \(25\) \(0\) \(q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.b \(1\) \(1.551\) \(\Q\) \(\Q(\sqrt{-15}) \) \(7\) \(-9\) \(-25\) \(0\) \(q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.c \(4\) \(1.551\) \(\Q(\sqrt{10}, \sqrt{-26})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)