Properties

Label 136.3.q
Level $136$
Weight $3$
Character orbit 136.q
Rep. character $\chi_{136}(5,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $272$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.q (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q(\zeta_{16})\)
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 304 304 0
Cusp forms 272 272 0
Eisenstein series 32 32 0

Trace form

\( 272 q - 8 q^{2} - 8 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{8} - 16 q^{9} + O(q^{10}) \) \( 272 q - 8 q^{2} - 8 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 8 q^{12} - 8 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} + 136 q^{24} - 16 q^{25} - 232 q^{26} + 232 q^{28} - 200 q^{30} - 16 q^{31} + 32 q^{32} + 56 q^{34} - 200 q^{36} + 192 q^{38} - 16 q^{39} - 456 q^{40} - 16 q^{41} + 424 q^{42} - 360 q^{44} + 200 q^{46} - 16 q^{47} - 80 q^{48} - 16 q^{49} - 16 q^{52} - 456 q^{54} - 16 q^{55} - 448 q^{56} - 336 q^{57} - 512 q^{58} - 736 q^{60} - 288 q^{62} - 16 q^{63} - 152 q^{64} + 144 q^{65} - 80 q^{66} + 80 q^{68} + 288 q^{70} - 16 q^{71} + 512 q^{72} + 464 q^{73} + 328 q^{74} + 496 q^{76} + 1136 q^{78} - 16 q^{79} + 520 q^{80} - 464 q^{81} + 592 q^{82} + 1184 q^{86} - 16 q^{87} - 840 q^{88} - 16 q^{89} + 1512 q^{90} - 1016 q^{92} + 664 q^{94} - 16 q^{95} - 768 q^{96} - 16 q^{97} + 400 q^{98} + O(q^{100}) \)

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.q.a 136.q 136.q $272$ $3.706$ None \(-8\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{16}]$