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Properties

Label 136.2.c
Level $136$
Weight $2$
Character orbit 136.c
Rep. character $\chi_{136}(69,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $36$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 136.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(136, [\chi])\).

Total New Old
Modular forms 20 16 4
Cusp forms 16 16 0
Eisenstein series 4 0 4

Trace form

\( 16 q - 2 q^{2} + 2 q^{4} + 6 q^{6} - 4 q^{7} - 2 q^{8} - 16 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{2} + 2 q^{4} + 6 q^{6} - 4 q^{7} - 2 q^{8} - 16 q^{9} - 2 q^{10} + 14 q^{12} - 4 q^{14} + 2 q^{16} - 10 q^{18} - 2 q^{20} - 10 q^{22} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 20 q^{26} - 16 q^{28} + 16 q^{30} + 12 q^{31} - 2 q^{32} - 30 q^{36} - 12 q^{38} + 8 q^{39} + 22 q^{40} + 8 q^{42} - 6 q^{44} - 44 q^{46} - 24 q^{47} - 22 q^{48} + 2 q^{50} - 12 q^{52} + 16 q^{54} + 32 q^{55} - 12 q^{56} + 16 q^{57} + 2 q^{58} + 56 q^{60} + 36 q^{62} + 20 q^{63} + 26 q^{64} + 12 q^{66} + 40 q^{70} - 36 q^{71} - 34 q^{72} + 16 q^{73} - 46 q^{74} + 4 q^{76} + 28 q^{78} - 20 q^{79} - 50 q^{80} + 20 q^{82} + 40 q^{84} - 8 q^{86} + 32 q^{87} + 22 q^{88} + 16 q^{89} - 14 q^{90} - 12 q^{92} - 64 q^{94} + 16 q^{95} + 58 q^{96} - 66 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(136, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
136.2.c.a 136.c 8.b $8$ $1.086$ 8.0.1649659456.5 None \(-1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
136.2.c.b 136.c 8.b $8$ $1.086$ 8.0.4469724736.1 None \(-1\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)