Properties

Label 40.4.c
Level $40$
Weight $4$
Character orbit 40.c
Rep. character $\chi_{40}(9,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(40, [\chi])\).

Total New Old
Modular forms 22 4 18
Cusp forms 14 4 10
Eisenstein series 8 0 8

Trace form

\( 4 q - 4 q^{5} - 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{5} - 4 q^{9} + 80 q^{11} - 80 q^{15} - 80 q^{19} - 272 q^{21} + 276 q^{25} + 280 q^{29} + 384 q^{31} - 304 q^{35} - 224 q^{39} - 1048 q^{41} + 772 q^{45} + 492 q^{49} + 1920 q^{51} - 1616 q^{55} - 1392 q^{59} - 1384 q^{61} + 608 q^{65} + 112 q^{69} + 1376 q^{71} + 160 q^{75} + 1472 q^{79} - 1484 q^{81} + 1152 q^{85} + 1320 q^{89} + 992 q^{91} - 1456 q^{95} - 3152 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(40, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.4.c.a 40.c 5.b $4$ $2.360$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(40, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(40, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)