Properties

Label 40.11.g
Level $40$
Weight $11$
Character orbit 40.g
Rep. character $\chi_{40}(11,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $1$
Sturm bound $66$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 40.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(66\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(40, [\chi])\).

Total New Old
Modular forms 62 40 22
Cusp forms 58 40 18
Eisenstein series 4 0 4

Trace form

\( 40 q - 22 q^{2} - 1864 q^{4} - 19644 q^{6} - 3448 q^{8} + 787320 q^{9} - 31250 q^{10} - 91808 q^{11} - 111340 q^{12} + 371356 q^{14} + 2799880 q^{16} - 974678 q^{18} - 5107040 q^{19} - 1187500 q^{20} - 21770780 q^{22}+ \cdots + 19036908320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{11}^{\mathrm{new}}(40, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.11.g.a 40.g 8.d $40$ $25.414$ None 40.11.g.a \(-22\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{11}^{\mathrm{old}}(40, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(40, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)