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Properties

Label 126.10.k
Level $126$
Weight $10$
Character orbit 126.k
Rep. character $\chi_{126}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(126, [\chi])\).

Total New Old
Modular forms 448 48 400
Cusp forms 416 48 368
Eisenstein series 32 0 32

Trace form

\( 48 q + 6144 q^{4} - 12720 q^{7} + O(q^{10}) \) \( 48 q + 6144 q^{4} - 12720 q^{7} + 153792 q^{10} - 1572864 q^{16} - 2546532 q^{19} + 4853376 q^{22} - 6871164 q^{25} + 2380800 q^{28} - 6720912 q^{31} + 1881660 q^{37} + 39370752 q^{40} - 171303864 q^{43} + 54125568 q^{46} + 129836928 q^{49} - 58125312 q^{52} + 180566208 q^{58} - 632749248 q^{61} - 805306368 q^{64} + 721189428 q^{67} + 308075328 q^{70} - 853713108 q^{73} + 1452429384 q^{79} - 1355242752 q^{82} + 368938080 q^{85} + 621232128 q^{88} + 4577539644 q^{91} - 1279193472 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.10.k.a 126.k 21.g $48$ $64.895$ None \(0\) \(0\) \(0\) \(-12720\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{10}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)