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Properties

Label 126.2.k
Level $126$
Weight $2$
Character orbit 126.k
Rep. character $\chi_{126}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

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

\( 8 q + 4 q^{4} + 4 q^{7} + O(q^{10}) \) \( 8 q + 4 q^{4} + 4 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} - 24 q^{22} - 16 q^{25} - 4 q^{28} - 12 q^{31} - 16 q^{37} + 12 q^{40} + 32 q^{43} + 20 q^{49} + 12 q^{58} + 24 q^{61} - 8 q^{64} + 40 q^{67} - 12 q^{70} + 24 q^{73} + 28 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} - 24 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.2.k.a 126.k 21.g $8$ $1.006$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{24}-\zeta_{24}^{3})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)

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

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