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Properties

Label 124.2.f
Level $124$
Weight $2$
Character orbit 124.f
Rep. character $\chi_{124}(33,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $8$
Newform subspaces $2$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 124.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 76 8 68
Cusp forms 52 8 44
Eisenstein series 24 0 24

Trace form

\( 8 q + 2 q^{3} + 2 q^{5} + 8 q^{7} + 2 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{3} + 2 q^{5} + 8 q^{7} + 2 q^{9} - 5 q^{11} - 3 q^{13} - 11 q^{15} + 4 q^{17} + 6 q^{19} - 12 q^{21} - 10 q^{25} - 4 q^{27} - 12 q^{29} - 15 q^{31} - 7 q^{33} - 16 q^{35} - 8 q^{37} - 16 q^{39} + 3 q^{41} - 10 q^{43} + 16 q^{45} + 26 q^{47} + 14 q^{49} + 12 q^{51} - 32 q^{53} + 16 q^{55} + 78 q^{57} + 34 q^{59} + 8 q^{61} - 20 q^{63} + 5 q^{65} + 36 q^{67} + 38 q^{69} + 20 q^{71} - 20 q^{73} - 12 q^{75} - 19 q^{77} + 7 q^{79} + 27 q^{81} - 13 q^{83} - 12 q^{85} - 48 q^{89} - q^{91} - 43 q^{93} - 33 q^{95} + 4 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
124.2.f.a 124.f 31.d $4$ $0.990$ \(\Q(\zeta_{10})\) None \(0\) \(-3\) \(8\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{3}+2q^{5}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
124.2.f.b 124.f 31.d $4$ $0.990$ \(\Q(\zeta_{10})\) None \(0\) \(5\) \(-6\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)

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

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