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Properties

Label 124.3.o
Level $124$
Weight $3$
Character orbit 124.o
Rep. character $\chi_{124}(13,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $40$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 124.o (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(124, [\chi])\).

Total New Old
Modular forms 280 40 240
Cusp forms 232 40 192
Eisenstein series 48 0 48

Trace form

\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + O(q^{10}) \) \( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + 2 q^{11} - 18 q^{13} + 35 q^{15} + 25 q^{17} - 11 q^{19} + 54 q^{21} + 25 q^{23} - 75 q^{25} + 225 q^{27} + 20 q^{29} + 59 q^{31} - 303 q^{33} - 66 q^{35} - 222 q^{37} - 169 q^{39} + q^{41} + 122 q^{43} + 54 q^{45} - 120 q^{47} - 118 q^{49} - 515 q^{51} + 61 q^{53} - 121 q^{55} - 201 q^{57} - 257 q^{59} - 158 q^{63} + 182 q^{65} - q^{67} + 510 q^{69} + 459 q^{71} + 253 q^{73} + 651 q^{75} + 670 q^{77} + 385 q^{79} + 974 q^{81} + 375 q^{83} - 370 q^{85} - 344 q^{87} + 245 q^{89} + 960 q^{91} - 212 q^{93} - 851 q^{95} - 797 q^{97} - 21 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(124, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
124.3.o.a 124.o 31.h $40$ $3.379$ None \(0\) \(-3\) \(-3\) \(19\) $\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{3}^{\mathrm{old}}(124, [\chi])\) into lower level spaces

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