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Properties

Label 140.5.n
Level $140$
Weight $5$
Character orbit 140.n
Rep. character $\chi_{140}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 140.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(140, [\chi])\).

Total New Old
Modular forms 204 32 172
Cusp forms 180 32 148
Eisenstein series 24 0 24

Trace form

\( 32 q - 27 q^{5} - 414 q^{9} + O(q^{10}) \) \( 32 q - 27 q^{5} - 414 q^{9} + 180 q^{11} + 446 q^{15} + 516 q^{19} + 742 q^{21} + 393 q^{25} - 1248 q^{29} + 3606 q^{31} + 2469 q^{35} + 2364 q^{39} - 6528 q^{45} - 1208 q^{49} + 830 q^{51} + 4518 q^{59} - 8250 q^{61} - 6084 q^{65} + 23304 q^{71} - 28671 q^{75} - 4306 q^{79} - 19892 q^{81} + 34022 q^{85} + 28386 q^{89} - 11768 q^{91} - 2343 q^{95} - 90820 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(140, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
140.5.n.a 140.n 35.i $32$ $14.472$ None \(0\) \(0\) \(-27\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{5}^{\mathrm{old}}(140, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)