↑

Properties

Label 124.6.f
Level $124$
Weight $6$
Character orbit 124.f
Rep. character $\chi_{124}(33,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $56$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 124.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(124, [\chi])\).

Total New Old
Modular forms 332 56 276
Cusp forms 308 56 252
Eisenstein series 24 0 24

Trace form

\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} + O(q^{10}) \) \( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(124, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
124.6.f.a 124.f 31.d $56$ $19.888$ None \(0\) \(2\) \(-58\) \(104\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{6}^{\mathrm{old}}(124, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(124, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)