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Properties

Label 40.6.c
Level $40$
Weight $6$
Character orbit 40.c
Rep. character $\chi_{40}(9,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(40, [\chi])\).

Total New Old
Modular forms 34 8 26
Cusp forms 26 8 18
Eisenstein series 8 0 8

Trace form

\( 8 q + 8 q^{5} - 1000 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{5} - 1000 q^{9} - 736 q^{11} - 992 q^{15} + 1376 q^{19} + 1984 q^{21} - 2136 q^{25} + 5872 q^{29} + 4224 q^{31} + 19232 q^{35} - 3008 q^{39} + 23600 q^{41} - 28328 q^{45} - 45000 q^{49} - 124800 q^{51} + 15008 q^{55} + 91680 q^{59} + 123856 q^{61} - 72064 q^{65} - 76736 q^{69} - 125632 q^{71} + 222784 q^{75} + 43264 q^{79} + 409672 q^{81} - 293760 q^{85} - 41904 q^{89} - 487616 q^{91} + 442592 q^{95} + 266848 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(40, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.6.c.a 40.c 5.b $8$ $6.415$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(\beta _{2}+\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(40, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(40, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)