Properties

Label 30.2.c
Level $30$
Weight $2$
Character orbit 30.c
Rep. character $\chi_{30}(19,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(30, [\chi])\) into newform subspaces

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 \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)