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Properties

Label 124.4.a
Level $124$
Weight $4$
Character orbit 124.a
Rep. character $\chi_{124}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $64$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 124.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(124))\).

Total New Old
Modular forms 51 8 43
Cusp forms 45 8 37
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(31\)FrickeDim
\(-\)\(+\)$-$\(4\)
\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(4\)
Minus space\(-\)\(4\)

Trace form

\( 8 q - 2 q^{3} - 8 q^{5} + 4 q^{7} + 40 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{3} - 8 q^{5} + 4 q^{7} + 40 q^{9} - 2 q^{11} - 86 q^{13} + 20 q^{15} - 88 q^{17} + 64 q^{19} + 32 q^{21} - 72 q^{23} + 252 q^{25} - 224 q^{27} + 94 q^{29} - 120 q^{33} - 48 q^{35} + 314 q^{37} + 212 q^{39} - 308 q^{41} - 518 q^{43} + 120 q^{45} + 500 q^{47} + 132 q^{49} + 596 q^{51} + 38 q^{53} - 596 q^{55} + 60 q^{57} - 540 q^{59} - 870 q^{61} - 92 q^{63} + 224 q^{65} + 40 q^{67} - 216 q^{69} + 968 q^{71} + 704 q^{73} + 210 q^{75} - 1996 q^{77} - 188 q^{79} + 160 q^{81} + 234 q^{83} + 1604 q^{85} - 540 q^{87} - 268 q^{89} + 508 q^{91} + 186 q^{93} - 856 q^{95} + 60 q^{97} + 2938 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(124))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 31
124.4.a.a 124.a 1.a $4$ $7.316$ 4.4.841724.1 None \(0\) \(-4\) \(-14\) \(-12\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+(-3-\beta _{1}-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
124.4.a.b 124.a 1.a $4$ $7.316$ 4.4.4000044.1 None \(0\) \(2\) \(6\) \(16\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(124))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(124)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 2}\)