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Properties

Label 126.6.g
Level $126$
Weight $6$
Character orbit 126.g
Rep. character $\chi_{126}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $10$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(126, [\chi])\).

Total New Old
Modular forms 256 32 224
Cusp forms 224 32 192
Eisenstein series 32 0 32

Trace form

\( 32 q - 256 q^{4} + 72 q^{5} + 236 q^{7} + 48 q^{10} - 528 q^{11} - 560 q^{13} + 432 q^{14} - 4096 q^{16} + 384 q^{17} - 3392 q^{19} - 2304 q^{20} + 1920 q^{22} - 5052 q^{23} - 7360 q^{25} + 6960 q^{26}+ \cdots - 102528 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.6.g.a 126.g 7.c $2$ $20.208$ \(\Q(\sqrt{-3}) \) None 126.6.g.a \(-4\) \(0\) \(-12\) \(119\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+(-12+\cdots)q^{5}+\cdots\)
126.6.g.b 126.g 7.c $2$ $20.208$ \(\Q(\sqrt{-3}) \) None 42.6.e.b \(-4\) \(0\) \(86\) \(49\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+(86-86\zeta_{6})q^{5}+\cdots\)
126.6.g.c 126.g 7.c $2$ $20.208$ \(\Q(\sqrt{-3}) \) None 42.6.e.a \(4\) \(0\) \(-6\) \(119\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+(-6+6\zeta_{6})q^{5}+\cdots\)
126.6.g.d 126.g 7.c $2$ $20.208$ \(\Q(\sqrt{-3}) \) None 126.6.g.a \(4\) \(0\) \(12\) \(119\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+(12-12\zeta_{6})q^{5}+\cdots\)
126.6.g.e 126.g 7.c $4$ $20.208$ \(\Q(\sqrt{-3}, \sqrt{130})\) None 14.6.c.b \(-8\) \(0\) \(-42\) \(232\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{1}q^{2}+(-2^{4}-2^{4}\beta _{1})q^{4}+21\beta _{1}q^{5}+\cdots\)
126.6.g.f 126.g 7.c $4$ $20.208$ \(\Q(\sqrt{-3}, \sqrt{697})\) None 126.6.g.f \(-8\) \(0\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\beta _{2})q^{2}-2^{4}\beta _{2}q^{4}+(-6+\cdots)q^{5}+\cdots\)
126.6.g.g 126.g 7.c $4$ $20.208$ \(\Q(\sqrt{-3}, \sqrt{505})\) None 42.6.e.d \(-8\) \(0\) \(17\) \(-408\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{1}q^{2}+(-2^{4}+2^{4}\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
126.6.g.h 126.g 7.c $4$ $20.208$ \(\Q(\sqrt{-3}, \sqrt{9601})\) None 42.6.e.c \(8\) \(0\) \(-53\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{2}q^{2}+(-2^{4}+2^{4}\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
126.6.g.i 126.g 7.c $4$ $20.208$ \(\Q(\sqrt{-3}, \sqrt{697})\) None 126.6.g.f \(8\) \(0\) \(7\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\beta _{2})q^{2}-2^{4}\beta _{2}q^{4}+(6-5\beta _{1}+\cdots)q^{5}+\cdots\)
126.6.g.j 126.g 7.c $4$ $20.208$ \(\Q(\sqrt{-3}, \sqrt{79})\) None 14.6.c.a \(8\) \(0\) \(70\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4+4\beta _{2})q^{2}+2^{4}\beta _{2}q^{4}+(35+4\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)