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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
126.2.e.a \(2\) \(1.006\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-4\) \(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}-3\zeta_{6}q^{5}+\cdots\)
126.2.e.b \(2\) \(1.006\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(-4\) \(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots\)
126.2.e.c \(6\) \(1.006\) 6.0.309123.1 None \(-6\) \(2\) \(1\) \(2\) \(q-q^{2}+(-\beta _{2}-\beta _{4})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
126.2.e.d \(6\) \(1.006\) 6.0.309123.1 None \(6\) \(-2\) \(-5\) \(4\) \(q+q^{2}+(\beta _{3}-\beta _{4}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)