↑

Properties

Label 57.3.k
Level $57$
Weight $3$
Character orbit 57.k
Rep. character $\chi_{57}(10,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $42$
Newform subspaces $2$
Sturm bound $20$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 57.k (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(57, [\chi])\).

Total New Old
Modular forms 90 42 48
Cusp forms 66 42 24
Eisenstein series 24 0 24

Trace form

\( 42 q - 6 q^{4} + 18 q^{6} - 18 q^{7} + O(q^{10}) \) \( 42 q - 6 q^{4} + 18 q^{6} - 18 q^{7} - 84 q^{10} + 30 q^{11} - 72 q^{12} + 3 q^{13} - 6 q^{14} - 36 q^{15} - 6 q^{16} - 60 q^{17} + 39 q^{19} + 156 q^{20} - 9 q^{21} + 48 q^{22} + 48 q^{23} + 144 q^{24} + 168 q^{25} + 96 q^{26} + 27 q^{27} - 156 q^{28} - 252 q^{29} - 216 q^{31} - 438 q^{32} - 54 q^{33} - 210 q^{34} + 108 q^{35} + 18 q^{36} - 228 q^{38} + 186 q^{40} + 24 q^{41} + 72 q^{42} + 261 q^{43} + 564 q^{44} - 18 q^{45} + 450 q^{46} + 510 q^{47} - 72 q^{48} - 15 q^{49} + 702 q^{50} + 144 q^{51} - 342 q^{52} - 90 q^{53} - 54 q^{54} - 66 q^{55} + 144 q^{57} + 120 q^{58} - 162 q^{59} - 36 q^{60} - 36 q^{61} - 684 q^{62} - 108 q^{63} + 162 q^{64} - 1080 q^{65} - 432 q^{66} - 243 q^{67} - 450 q^{68} - 432 q^{69} + 60 q^{70} - 108 q^{72} - 45 q^{73} - 384 q^{74} + 168 q^{76} + 72 q^{77} + 360 q^{78} - 90 q^{79} - 1134 q^{80} - 546 q^{82} + 378 q^{83} + 972 q^{84} + 78 q^{85} + 600 q^{86} + 288 q^{87} - 144 q^{88} + 672 q^{89} + 18 q^{90} + 282 q^{91} + 1488 q^{92} + 504 q^{93} + 126 q^{95} - 432 q^{96} - 174 q^{97} + 300 q^{98} + 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(57, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.3.k.a 57.k 19.f $18$ $1.553$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(9\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$ \(q+(1+\beta _{8}+\beta _{9}-\beta _{13}+\beta _{14})q^{2}+(-2\beta _{3}+\cdots)q^{3}+\cdots\)
57.3.k.b 57.k 19.f $24$ $1.553$ None \(-9\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(57, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(57, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)