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Properties

Label 126.2.h
Level $126$
Weight $2$
Character orbit 126.h
Rep. character $\chi_{126}(67,\cdot)$
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.h (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

\( 16 q - 8 q^{4} + 8 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{4} + 8 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} - 8 q^{11} + 2 q^{13} + 2 q^{14} + 10 q^{15} - 8 q^{16} - 14 q^{17} + 12 q^{18} - 4 q^{19} - 4 q^{20} - 14 q^{21} + 4 q^{23} + 2 q^{24} + 16 q^{25} - 16 q^{26} - 2 q^{28} - 10 q^{29} + 10 q^{30} + 2 q^{31} + 2 q^{33} - 14 q^{35} - 8 q^{36} + 2 q^{37} + 24 q^{38} - 2 q^{39} - 6 q^{41} - 6 q^{42} + 2 q^{43} + 4 q^{44} - 28 q^{45} - 6 q^{46} - 6 q^{47} - 14 q^{49} - 4 q^{50} + 8 q^{51} - 4 q^{52} + 24 q^{53} + 2 q^{54} - 12 q^{55} - 4 q^{56} + 18 q^{57} - 12 q^{58} - 22 q^{59} + 10 q^{60} + 8 q^{61} + 44 q^{62} + 42 q^{63} + 16 q^{64} - 6 q^{65} + 8 q^{66} + 14 q^{67} + 28 q^{68} + 38 q^{69} + 52 q^{71} - 28 q^{73} + 12 q^{74} - 74 q^{75} - 4 q^{76} - 34 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{80} - 26 q^{81} + 16 q^{83} + 22 q^{84} + 12 q^{85} - 24 q^{86} - 56 q^{87} - 36 q^{89} + 2 q^{90} - 16 q^{91} - 2 q^{92} + 46 q^{93} + 12 q^{94} + 34 q^{95} + 2 q^{96} + 2 q^{97} - 24 q^{98} - 62 q^{99} + O(q^{100}) \)

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.h.a 126.h 63.g $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.h.b 126.h 63.g $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(6\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.h.c 126.h 63.g $6$ $1.006$ 6.0.309123.1 None \(-3\) \(4\) \(10\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(1-\beta _{5})q^{3}+(-1-\beta _{4})q^{4}+\cdots\)
126.2.h.d 126.h 63.g $6$ $1.006$ 6.0.309123.1 None \(3\) \(2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)

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

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