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Properties

Label 126.3.c
Level $126$
Weight $3$
Character orbit 126.c
Rep. character $\chi_{126}(55,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $72$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(126, [\chi])\).

Total New Old
Modular forms 56 8 48
Cusp forms 40 8 32
Eisenstein series 16 0 16

Trace form

\( 8 q + 16 q^{4} - 8 q^{7} + O(q^{10}) \) \( 8 q + 16 q^{4} - 8 q^{7} + 24 q^{11} + 24 q^{14} + 32 q^{16} + 48 q^{22} - 24 q^{23} - 136 q^{25} - 16 q^{28} - 120 q^{29} + 24 q^{35} - 16 q^{37} + 80 q^{43} + 48 q^{44} + 48 q^{46} - 88 q^{49} - 96 q^{50} + 216 q^{53} + 48 q^{56} - 192 q^{58} + 64 q^{64} - 240 q^{65} - 32 q^{67} - 192 q^{70} + 120 q^{71} - 288 q^{74} - 24 q^{77} + 544 q^{79} - 48 q^{85} + 240 q^{86} + 96 q^{88} + 528 q^{91} - 48 q^{92} + 240 q^{95} + 192 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.c.a 126.c 7.b $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-33})\) None 126.3.c.a \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+2q^{4}-\beta _{2}q^{5}+(-4+\beta _{3})q^{7}+\cdots\)
126.3.c.b 126.c 7.b $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 42.3.c.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+2q^{4}+(2\beta _{2}-\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

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