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Properties

Label 126.2.e
Level $126$
Weight $2$
Character orbit 126.e
Rep. character $\chi_{126}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $4$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(126, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\( 16 q + 16 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 8 q^{9} + O(q^{10}) \) \( 16 q + 16 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 8 q^{9} + 4 q^{11} + 2 q^{13} + 2 q^{14} + 10 q^{15} + 16 q^{16} - 14 q^{17} - 12 q^{18} - 4 q^{19} - 4 q^{20} - 20 q^{21} - 2 q^{23} - 4 q^{24} - 8 q^{25} - 16 q^{26} - 2 q^{28} - 10 q^{29} + 4 q^{30} - 4 q^{31} - 40 q^{33} - 14 q^{35} - 8 q^{36} + 2 q^{37} - 12 q^{38} + 16 q^{39} - 6 q^{41} - 12 q^{42} + 2 q^{43} + 4 q^{44} + 38 q^{45} - 6 q^{46} + 12 q^{47} + 4 q^{49} - 4 q^{50} + 14 q^{51} + 2 q^{52} + 24 q^{53} + 14 q^{54} - 12 q^{55} + 2 q^{56} + 18 q^{57} + 6 q^{58} + 44 q^{59} + 10 q^{60} - 16 q^{61} + 44 q^{62} + 24 q^{63} + 16 q^{64} + 12 q^{65} - 16 q^{66} - 28 q^{67} - 14 q^{68} + 38 q^{69} - 18 q^{70} + 52 q^{71} - 12 q^{72} - 28 q^{73} - 6 q^{74} + 76 q^{75} - 4 q^{76} + 50 q^{77} + 32 q^{78} - 40 q^{79} - 4 q^{80} + 4 q^{81} + 16 q^{83} - 20 q^{84} + 12 q^{85} + 12 q^{86} + 4 q^{87} - 36 q^{89} + 2 q^{90} - 16 q^{91} - 2 q^{92} - 38 q^{93} - 24 q^{94} - 68 q^{95} - 4 q^{96} + 2 q^{97} - 24 q^{98} - 62 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.2.e.a 126.e 63.h $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}-3\zeta_{6}q^{5}+\cdots\)
126.2.e.b 126.e 63.h $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots\)
126.2.e.c 126.e 63.h $6$ $1.006$ 6.0.309123.1 None \(-6\) \(2\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-\beta _{2}-\beta _{4})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
126.2.e.d 126.e 63.h $6$ $1.006$ 6.0.309123.1 None \(6\) \(-2\) \(-5\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(\beta _{3}-\beta _{4}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(126, [\chi]) \cong \)