Properties

Label 126.2.g
Level 126
Weight 2
Character orbit g
Rep. character \(\chi_{126}(37,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 8
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(126, [\chi])\) into irreducible Hecke orbits

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

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