Properties

Label 40.2.c
Level $40$
Weight $2$
Character orbit 40.c
Rep. character $\chi_{40}(9,\cdot)$
Character field $\Q$
Dimension $2$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
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 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\( 2q - 2q^{5} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{5} - 2q^{9} - 8q^{11} + 8q^{15} + 8q^{19} + 8q^{21} - 6q^{25} - 4q^{29} - 8q^{35} - 16q^{39} + 4q^{41} + 2q^{45} + 6q^{49} + 8q^{55} + 24q^{59} - 20q^{61} + 16q^{65} + 8q^{69} + 16q^{71} - 16q^{75} - 32q^{79} - 22q^{81} - 12q^{89} + 16q^{91} - 8q^{95} + 8q^{99} + O(q^{100}) \)

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.c.a \(2\) \(0.319\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1-i)q^{5}-iq^{7}-q^{9}+\cdots\)