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Properties

Label 40.5.i
Level $40$
Weight $5$
Character orbit 40.i
Rep. character $\chi_{40}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 40.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(40, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44 q - 2 q^{2} + 32 q^{6} - 4 q^{7} - 92 q^{8} + O(q^{10}) \) \( 44 q - 2 q^{2} + 32 q^{6} - 4 q^{7} - 92 q^{8} - 154 q^{10} + 196 q^{12} - 4 q^{15} + 72 q^{16} + 236 q^{17} + 682 q^{18} - 904 q^{20} - 740 q^{22} - 4 q^{23} + 332 q^{25} - 2236 q^{26} + 2740 q^{28} + 3940 q^{30} - 264 q^{31} - 4352 q^{32} + 320 q^{33} - 4580 q^{36} - 4684 q^{38} + 5276 q^{40} - 8 q^{41} + 6676 q^{42} + 6784 q^{46} - 5764 q^{47} - 4000 q^{48} - 674 q^{50} + 5556 q^{52} + 2496 q^{55} + 13304 q^{56} - 328 q^{57} - 804 q^{58} + 3740 q^{60} - 13984 q^{62} + 9924 q^{63} - 3700 q^{65} - 12248 q^{66} - 11700 q^{68} - 10820 q^{70} - 19976 q^{71} - 17572 q^{72} + 13196 q^{73} - 12344 q^{76} + 23104 q^{78} - 24624 q^{80} - 13812 q^{81} + 15116 q^{82} + 16400 q^{86} + 48952 q^{87} + 35920 q^{88} + 49926 q^{90} + 25020 q^{92} - 27848 q^{95} + 42176 q^{96} + 3276 q^{97} - 65998 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(40, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.5.i.a 40.i 40.i $44$ $4.135$ None 40.5.i.a \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$