Properties

Label 30.2.e
Level 30
Weight 2
Character orbit e
Rep. character \(\chi_{30}(17,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 30.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(30, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut -\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 8q^{18} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 4q^{36} \) \(\mathstrut +\mathstrut 24q^{37} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 4q^{48} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut -\mathstrut 4q^{60} \) \(\mathstrut -\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 16q^{67} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 28q^{75} \) \(\mathstrut +\mathstrut 16q^{76} \) \(\mathstrut +\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 8q^{85} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut +\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(30, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
30.2.e.a \(4\) \(0.240\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(-4\) \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)