Properties

Label 57.2.f
Level $57$
Weight $2$
Character orbit 57.f
Rep. character $\chi_{57}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $13$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 57.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(13\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(57, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8 q + 4 q^{6} - 16 q^{7} - 4 q^{9} - 12 q^{10} + 12 q^{13} + 4 q^{16} - 12 q^{21} + 12 q^{22} + 4 q^{24} - 12 q^{25} + 12 q^{28} - 8 q^{30} + 24 q^{33} + 24 q^{34} + 16 q^{39} - 12 q^{40} - 20 q^{42} - 16 q^{43}+ \cdots - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(57, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.2.f.a 57.f 57.f $8$ $0.455$ \(\Q(\zeta_{24})\) None 57.2.f.a \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)