Properties

Label 136.3.p
Level $136$
Weight $3$
Character orbit 136.p
Rep. character $\chi_{136}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $136$
Newform subspaces $3$
Sturm bound $54$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.p (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 3 \)
Sturm bound: \(54\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 152 152 0
Cusp forms 136 136 0
Eisenstein series 16 16 0

Trace form

\( 136 q - 4 q^{2} - 8 q^{3} - 28 q^{6} - 4 q^{8} - 8 q^{9} + O(q^{10}) \) \( 136 q - 4 q^{2} - 8 q^{3} - 28 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 32 q^{12} - 20 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 120 q^{19} - 68 q^{20} - 28 q^{22} - 216 q^{24} - 56 q^{25} + 92 q^{26} - 8 q^{27} - 188 q^{28} - 124 q^{32} - 16 q^{33} - 36 q^{34} - 16 q^{35} + 156 q^{36} + 304 q^{40} + 72 q^{41} - 16 q^{42} - 8 q^{43} + 236 q^{44} + 116 q^{46} + 12 q^{48} - 8 q^{49} + 352 q^{50} + 312 q^{51} - 136 q^{52} - 588 q^{54} - 196 q^{56} + 152 q^{57} - 480 q^{58} - 8 q^{59} - 312 q^{60} - 364 q^{62} - 288 q^{65} - 372 q^{66} - 16 q^{67} + 364 q^{68} + 528 q^{70} - 248 q^{73} + 332 q^{74} - 8 q^{75} - 40 q^{76} + 784 q^{78} + 152 q^{80} + 344 q^{82} - 968 q^{83} + 112 q^{84} - 1152 q^{86} + 808 q^{88} - 452 q^{90} - 400 q^{91} + 716 q^{92} - 88 q^{94} + 948 q^{96} - 8 q^{97} - 80 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
136.3.p.a $4$ $3.706$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) \(0\) \(-8\) \(0\) \(0\) \(q-2\zeta_{8}^{3}q^{2}+(-2-2\zeta_{8}-3\zeta_{8}^{2}+3\zeta_{8}^{3})q^{3}+\cdots\)
136.3.p.b $4$ $3.706$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) \(0\) \(8\) \(0\) \(0\) \(q-2\zeta_{8}^{3}q^{2}+(2+2\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
136.3.p.c $128$ $3.706$ None \(-4\) \(-8\) \(0\) \(0\)