Properties

Label 40.2.d
Level $40$
Weight $2$
Character orbit 40.d
Rep. character $\chi_{40}(21,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 40.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
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 4 4
Cusp forms 4 4 0
Eisenstein series 4 0 4

Trace form

\( 4q - 2q^{2} + 4q^{6} - 4q^{7} - 8q^{8} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 4q^{6} - 4q^{7} - 8q^{8} - 4q^{9} + 2q^{10} - 4q^{12} - 4q^{14} + 4q^{15} + 8q^{16} + 14q^{18} + 4q^{20} + 4q^{22} - 4q^{23} + 8q^{24} - 4q^{25} - 12q^{26} + 12q^{28} - 8q^{30} - 8q^{31} + 8q^{32} + 8q^{33} - 12q^{34} - 24q^{36} - 20q^{38} + 24q^{39} - 8q^{40} - 8q^{41} - 4q^{42} + 8q^{44} + 20q^{46} + 20q^{47} - 24q^{48} - 12q^{49} + 2q^{50} + 8q^{54} - 8q^{55} + 8q^{56} + 8q^{57} + 24q^{58} + 12q^{60} + 16q^{62} - 20q^{63} - 16q^{66} + 24q^{68} - 8q^{70} + 8q^{71} + 8q^{72} + 16q^{73} + 4q^{74} - 16q^{76} - 24q^{78} - 32q^{79} + 4q^{81} - 8q^{82} - 8q^{84} + 20q^{86} - 48q^{87} - 16q^{88} + 8q^{89} + 10q^{90} - 36q^{92} - 4q^{94} + 16q^{95} + 32q^{96} - 16q^{97} + 18q^{98} + O(q^{100}) \)

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.d.a \(4\) \(0.319\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-4\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)