Properties

Label 40.2.f
Level $40$
Weight $2$
Character orbit 40.f
Rep. character $\chi_{40}(29,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 40.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(40, [\chi])\).

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

Trace form

\( 4q - 4q^{4} - 4q^{6} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{4} - 4q^{6} - 4q^{9} + 4q^{10} + 12q^{14} - 8q^{15} - 8q^{16} + 12q^{20} + 16q^{24} - 4q^{25} - 12q^{30} + 16q^{31} - 24q^{34} + 4q^{36} - 16q^{40} - 24q^{44} - 12q^{46} + 4q^{49} + 24q^{50} + 16q^{54} + 24q^{55} + 8q^{60} + 32q^{64} + 24q^{66} - 12q^{70} - 48q^{71} - 24q^{74} + 24q^{76} - 16q^{79} - 24q^{80} - 20q^{81} - 24q^{84} + 12q^{86} + 24q^{89} - 4q^{90} + 36q^{94} - 24q^{95} - 16q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(40, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
40.2.f.a \(4\) \(0.319\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)