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

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

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.g.a \(2\) \(1.006\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
126.2.g.b \(2\) \(1.006\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(5\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
126.2.g.c \(2\) \(1.006\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
126.2.g.d \(2\) \(1.006\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(-1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)

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

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