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Properties

Label 40.2.k
Level $40$
Weight $2$
Character orbit 40.k
Rep. character $\chi_{40}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
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 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8} + O(q^{10}) \) \( 8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8} - 10 q^{10} - 8 q^{11} + 12 q^{12} + 8 q^{16} - 8 q^{17} + 10 q^{18} + 12 q^{22} + 20 q^{26} + 8 q^{27} - 20 q^{28} + 20 q^{30} - 32 q^{32} - 16 q^{33} + 20 q^{35} - 20 q^{36} - 4 q^{38} - 20 q^{40} - 8 q^{41} - 20 q^{42} + 28 q^{43} - 40 q^{46} + 16 q^{48} - 10 q^{50} + 8 q^{51} + 20 q^{52} + 40 q^{56} + 8 q^{57} + 20 q^{58} + 20 q^{60} + 40 q^{62} + 8 q^{66} - 28 q^{67} - 4 q^{68} + 20 q^{70} - 20 q^{72} + 16 q^{73} - 60 q^{75} - 8 q^{76} - 40 q^{78} + 32 q^{81} - 28 q^{82} - 44 q^{83} - 24 q^{86} + 16 q^{88} - 10 q^{90} - 40 q^{91} + 20 q^{92} + 32 q^{96} + 16 q^{97} - 6 q^{98} + O(q^{100}) \)

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.k.a 40.k 40.k $8$ $0.319$ \(\Q(\zeta_{20})\) None \(-2\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{20}^{7}q^{2}+(-1+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots\)