Properties

Label 40.2.j
Level $40$
Weight $2$
Character orbit 40.j
Rep. character $\chi_{40}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $0$
Newform subspaces $0$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
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 20 0 20
Cusp forms 4 0 4
Eisenstein series 16 0 16

Decomposition of \(S_{2}^{\mathrm{old}}(40, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(40, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)