Properties

Label 126.2.t
Level $126$
Weight $2$
Character orbit 126.t
Rep. character $\chi_{126}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

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

\( 16q + 8q^{4} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 16q + 8q^{4} + 2q^{7} - 6q^{9} - 6q^{13} - 6q^{14} - 18q^{15} - 8q^{16} + 18q^{17} + 12q^{18} - 18q^{21} - 6q^{24} + 16q^{25} - 12q^{26} - 36q^{27} - 2q^{28} + 6q^{29} - 18q^{30} + 6q^{31} + 18q^{33} - 30q^{35} - 2q^{37} - 30q^{39} + 6q^{41} + 30q^{42} - 2q^{43} + 12q^{44} + 12q^{45} + 6q^{46} - 18q^{47} + 10q^{49} - 12q^{50} + 36q^{53} + 18q^{54} + 6q^{57} - 12q^{58} + 30q^{59} - 6q^{60} - 60q^{61} - 36q^{62} + 42q^{63} - 16q^{64} + 42q^{65} + 48q^{66} + 14q^{67} + 36q^{68} + 42q^{69} + 30q^{75} - 18q^{77} - 16q^{79} + 54q^{81} - 18q^{84} - 12q^{85} - 48q^{87} + 24q^{89} - 18q^{90} - 12q^{91} + 6q^{92} + 30q^{93} - 66q^{95} - 6q^{96} - 6q^{97} + 24q^{98} + 18q^{99} + O(q^{100}) \)

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.t.a \(16\) \(1.006\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) \(q+(-\beta _{1}+\beta _{6})q^{2}+(-\beta _{11}-\beta _{14})q^{3}+\cdots\)

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

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