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Properties

Label 126.3.n
Level $126$
Weight $3$
Character orbit 126.n
Rep. character $\chi_{126}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $3$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(126, [\chi])\).

Total New Old
Modular forms 112 12 100
Cusp forms 80 12 68
Eisenstein series 32 0 32

Trace form

\( 12 q - 12 q^{4} - 6 q^{5} + 12 q^{7} + O(q^{10}) \) \( 12 q - 12 q^{4} - 6 q^{5} + 12 q^{7} - 24 q^{10} - 6 q^{11} + 12 q^{14} - 24 q^{16} + 78 q^{17} + 66 q^{19} - 72 q^{22} - 54 q^{23} + 24 q^{25} - 120 q^{26} - 36 q^{28} - 48 q^{29} + 18 q^{31} + 150 q^{35} + 54 q^{37} - 12 q^{38} + 48 q^{40} + 144 q^{43} - 12 q^{44} - 12 q^{46} - 42 q^{47} - 120 q^{49} + 288 q^{50} - 48 q^{52} - 42 q^{53} + 24 q^{58} + 102 q^{59} - 402 q^{61} + 96 q^{64} - 96 q^{65} + 114 q^{67} - 156 q^{68} + 180 q^{70} - 288 q^{71} - 30 q^{73} - 48 q^{74} - 246 q^{77} + 18 q^{79} + 24 q^{80} + 264 q^{82} - 420 q^{85} + 72 q^{88} + 450 q^{89} - 156 q^{91} + 216 q^{92} + 372 q^{94} + 162 q^{95} + 120 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.n.a 126.n 7.d $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-12\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2+2\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
126.3.n.b 126.n 7.d $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(2\beta _{1}+4\beta _{3})q^{5}+\cdots\)
126.3.n.c 126.n 7.d $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(6\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)