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Properties

Label 124.2.m
Level $124$
Weight $2$
Character orbit 124.m
Rep. character $\chi_{124}(9,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $24$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 124.m (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(124, [\chi])\).

Total New Old
Modular forms 152 24 128
Cusp forms 104 24 80
Eisenstein series 48 0 48

Trace form

\( 24 q - q^{3} + q^{5} - 9 q^{7} + 2 q^{9} + O(q^{10}) \) \( 24 q - q^{3} + q^{5} - 9 q^{7} + 2 q^{9} + 8 q^{11} + 2 q^{13} - q^{15} - q^{17} - q^{19} + 12 q^{21} - 21 q^{23} - 21 q^{25} - 43 q^{27} - 24 q^{29} - 29 q^{31} - 5 q^{33} + 10 q^{35} - 8 q^{37} - 17 q^{39} + 9 q^{41} - 2 q^{43} - 28 q^{45} - 38 q^{47} + 22 q^{49} + 69 q^{51} + 59 q^{53} - q^{55} - 7 q^{57} - 13 q^{59} + 36 q^{61} + 118 q^{63} + 94 q^{65} + 29 q^{67} + 52 q^{69} + 55 q^{71} + 55 q^{73} + 79 q^{75} - 38 q^{77} - 31 q^{79} - 98 q^{81} - 59 q^{83} - 60 q^{85} - 36 q^{87} - 57 q^{89} - 48 q^{91} - 124 q^{93} - 3 q^{95} - 19 q^{97} - 31 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(124, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
124.2.m.a 124.m 31.g $24$ $0.990$ None 124.2.m.a \(0\) \(-1\) \(1\) \(-9\) $\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(124, [\chi])\) into lower level spaces

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