Properties

Label 126.2.f
Level $126$
Weight $2$
Character orbit 126.f
Rep. character $\chi_{126}(43,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $4$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(126, [\chi])\).

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

Trace form

\( 12 q + 2 q^{2} + 6 q^{3} - 6 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{11} + 4 q^{14} - 8 q^{15} - 6 q^{16} + 4 q^{17} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 18 q^{25}+ \cdots + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.2.f.a 126.f 9.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None 126.2.f.a \(1\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.f.b 126.f 9.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None 126.2.f.b \(1\) \(3\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.f.c 126.f 9.c $4$ $1.006$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 126.2.f.c \(-2\) \(4\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
126.2.f.d 126.f 9.c $4$ $1.006$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 126.2.f.d \(2\) \(-1\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)