Properties

Label 136.3.f
Level $136$
Weight $3$
Character orbit 136.f
Rep. character $\chi_{136}(35,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(136, [\chi])\).

Total New Old
Modular forms 38 32 6
Cusp forms 34 32 2
Eisenstein series 4 0 4

Trace form

\( 32 q + 2 q^{2} - 6 q^{4} - 6 q^{6} + 14 q^{8} + 96 q^{9} + O(q^{10}) \) \( 32 q + 2 q^{2} - 6 q^{4} - 6 q^{6} + 14 q^{8} + 96 q^{9} + 26 q^{10} - 32 q^{11} + 6 q^{12} + 44 q^{14} - 30 q^{16} + 2 q^{18} - 10 q^{20} + 58 q^{22} - 54 q^{24} - 160 q^{25} + 52 q^{26} - 96 q^{27} + 16 q^{28} + 96 q^{30} - 18 q^{32} + 96 q^{35} - 14 q^{36} - 252 q^{38} + 198 q^{40} - 88 q^{42} - 32 q^{43} - 198 q^{44} - 52 q^{46} - 174 q^{48} - 256 q^{49} + 70 q^{50} + 172 q^{52} - 104 q^{54} + 76 q^{56} - 96 q^{57} - 226 q^{58} + 288 q^{59} - 40 q^{60} + 148 q^{62} - 198 q^{64} - 268 q^{66} - 128 q^{67} - 184 q^{70} + 214 q^{72} + 160 q^{73} + 246 q^{74} + 160 q^{75} + 316 q^{76} - 156 q^{78} + 94 q^{80} + 256 q^{81} - 236 q^{82} + 160 q^{83} + 24 q^{84} + 320 q^{86} + 374 q^{88} - 96 q^{89} + 158 q^{90} + 388 q^{92} + 64 q^{94} - 350 q^{96} + 256 q^{97} - 62 q^{98} - 224 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(136, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
136.3.f.a 136.f 8.d $32$ $3.706$ None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(136, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(136, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)