Properties

Label 30.3.b
Level 30
Weight 3
Character orbit b
Rep. character \(\chi_{30}(29,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 30.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(30, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\(4q \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 32q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 32q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 48q^{19} \) \(\mathstrut +\mathstrut 68q^{21} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut -\mathstrut 36q^{25} \) \(\mathstrut +\mathstrut 68q^{30} \) \(\mathstrut -\mathstrut 128q^{31} \) \(\mathstrut -\mathstrut 64q^{34} \) \(\mathstrut -\mathstrut 64q^{36} \) \(\mathstrut -\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut 68q^{45} \) \(\mathstrut +\mathstrut 136q^{46} \) \(\mathstrut +\mathstrut 60q^{49} \) \(\mathstrut +\mathstrut 32q^{51} \) \(\mathstrut +\mathstrut 100q^{54} \) \(\mathstrut +\mathstrut 272q^{55} \) \(\mathstrut +\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 64q^{61} \) \(\mathstrut +\mathstrut 32q^{64} \) \(\mathstrut -\mathstrut 272q^{66} \) \(\mathstrut -\mathstrut 68q^{69} \) \(\mathstrut -\mathstrut 136q^{70} \) \(\mathstrut -\mathstrut 272q^{75} \) \(\mathstrut +\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 288q^{79} \) \(\mathstrut +\mathstrut 188q^{81} \) \(\mathstrut +\mathstrut 136q^{84} \) \(\mathstrut +\mathstrut 128q^{85} \) \(\mathstrut +\mathstrut 128q^{90} \) \(\mathstrut -\mathstrut 200q^{94} \) \(\mathstrut -\mathstrut 16q^{96} \) \(\mathstrut +\mathstrut 272q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(30, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
30.3.b.a \(4\) \(0.817\) \(\Q(\sqrt{2}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(30, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)