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

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

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.k.a \(8\) \(0.319\) \(\Q(\zeta_{20})\) None \(-2\) \(-4\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{2}+(-1+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots\)