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Properties

Label 126.2.g
Level $126$
Weight $2$
Character orbit 126.g
Rep. character $\chi_{126}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $4$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 64 8 56
Cusp forms 32 8 24
Eisenstein series 32 0 32

Trace form

\( 8 q - 4 q^{4} + 4 q^{5} + 4 q^{7} + O(q^{10}) \) \( 8 q - 4 q^{4} + 4 q^{5} + 4 q^{7} - 4 q^{10} + 8 q^{11} - 8 q^{14} - 4 q^{16} - 4 q^{17} - 8 q^{19} - 8 q^{20} - 8 q^{22} - 4 q^{23} - 8 q^{25} + 4 q^{26} + 4 q^{28} - 8 q^{29} + 12 q^{31} + 16 q^{34} + 8 q^{35} + 16 q^{37} + 12 q^{38} - 4 q^{40} - 32 q^{43} + 8 q^{44} + 16 q^{46} - 12 q^{47} - 28 q^{49} + 16 q^{50} - 12 q^{53} - 8 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} + 8 q^{64} - 12 q^{65} + 8 q^{67} - 4 q^{68} + 28 q^{70} + 8 q^{71} - 16 q^{73} - 12 q^{74} + 16 q^{76} + 28 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} + 64 q^{85} + 12 q^{86} + 4 q^{88} - 24 q^{91} + 8 q^{92} - 24 q^{94} - 4 q^{95} - 40 q^{97} - 24 q^{98} + O(q^{100}) \)

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.g.a 126.g 7.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
126.2.g.b 126.g 7.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
126.2.g.c 126.g 7.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
126.2.g.d 126.g 7.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)