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Properties

Label 126.4.k
Level $126$
Weight $4$
Character orbit 126.k
Rep. character $\chi_{126}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(126, [\chi])\).

Total New Old
Modular forms 160 16 144
Cusp forms 128 16 112
Eisenstein series 32 0 32

Trace form

\( 16 q + 32 q^{4} - 64 q^{7} + O(q^{10}) \) \( 16 q + 32 q^{4} - 64 q^{7} + 72 q^{10} - 128 q^{16} + 684 q^{19} - 48 q^{22} - 212 q^{25} + 16 q^{28} - 1248 q^{31} + 1252 q^{37} + 288 q^{40} - 1112 q^{43} + 672 q^{46} - 1088 q^{49} - 336 q^{52} + 552 q^{58} + 3264 q^{61} - 1024 q^{64} + 68 q^{67} - 888 q^{70} - 3132 q^{73} + 2744 q^{79} - 864 q^{82} - 672 q^{85} - 96 q^{88} - 5748 q^{91} - 2160 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.4.k.a 126.k 21.g $16$ $7.434$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-64\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{12}q^{2}+(4-4\beta _{1})q^{4}+(-2\beta _{4}+\beta _{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

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