Properties

Label 126.2.l
Level $126$
Weight $2$
Character orbit 126.l
Rep. character $\chi_{126}(5,\cdot)$
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.l (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

\( 16q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 16q - 16q^{4} + 2q^{7} + 12q^{11} + 6q^{13} - 6q^{14} - 18q^{15} + 16q^{16} - 18q^{17} - 12q^{18} - 12q^{21} - 6q^{23} - 8q^{25} + 12q^{26} + 36q^{27} - 2q^{28} + 6q^{29} + 30q^{35} - 2q^{37} - 12q^{39} - 6q^{41} - 2q^{43} - 12q^{44} - 30q^{45} + 6q^{46} - 36q^{47} - 8q^{49} - 12q^{50} + 6q^{51} - 6q^{52} - 36q^{53} + 18q^{54} + 6q^{56} + 6q^{57} + 6q^{58} + 60q^{59} + 18q^{60} + 36q^{62} + 36q^{63} - 16q^{64} + 24q^{66} - 28q^{67} + 18q^{68} - 42q^{69} - 18q^{70} + 12q^{72} + 18q^{74} + 60q^{75} - 42q^{77} + 32q^{79} - 36q^{81} + 12q^{84} - 12q^{85} + 24q^{86} - 24q^{87} - 24q^{89} + 18q^{90} - 12q^{91} + 6q^{92} - 42q^{93} + 6q^{97} - 24q^{98} + 18q^{99} + O(q^{100}) \)

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.l.a \(16\) \(1.006\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{6}q^{2}-\beta _{11}q^{3}-q^{4}+(1+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)

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

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