Properties

Label 30.2.c
Level 30
Weight 2
Character orbit c
Rep. character \(\chi_{30}(19,\cdot)\)
Character field \(\Q\)
Dimension 2
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
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 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 2q^{36} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.c.a \(2\) \(0.240\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)