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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.2.d.a 40.d 8.b $4$ $0.319$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)