Properties

Label 126.3.p
Level $126$
Weight $3$
Character orbit 126.p
Rep. character $\chi_{126}(103,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32 q + 64 q^{4} - 2 q^{7} + 12 q^{9} + O(q^{10}) \) \( 32 q + 64 q^{4} - 2 q^{7} + 12 q^{9} - 12 q^{11} + 30 q^{13} - 12 q^{14} + 30 q^{15} + 128 q^{16} + 54 q^{17} - 12 q^{21} - 42 q^{23} + 80 q^{25} - 72 q^{26} - 126 q^{27} - 4 q^{28} - 84 q^{29} - 36 q^{30} - 66 q^{35} + 24 q^{36} - 22 q^{37} - 102 q^{39} - 396 q^{41} - 168 q^{42} - 16 q^{43} - 24 q^{44} - 156 q^{45} + 12 q^{46} + 50 q^{49} - 96 q^{50} - 54 q^{51} + 60 q^{52} - 252 q^{53} - 144 q^{54} - 24 q^{56} - 318 q^{57} - 24 q^{58} + 60 q^{60} + 186 q^{63} + 256 q^{64} + 12 q^{65} + 96 q^{66} - 140 q^{67} + 108 q^{68} + 210 q^{69} + 72 q^{70} + 300 q^{71} - 72 q^{74} + 582 q^{75} + 570 q^{77} + 96 q^{78} - 212 q^{79} + 468 q^{81} + 756 q^{83} - 24 q^{84} - 60 q^{85} - 120 q^{86} + 876 q^{87} + 414 q^{89} - 360 q^{90} - 186 q^{91} - 84 q^{92} + 426 q^{93} + 1104 q^{95} - 114 q^{97} - 96 q^{98} + 90 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.p.a $32$ $3.433$ None \(0\) \(0\) \(0\) \(-2\)

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

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