↑

Properties

Label 136.2.n
Level $136$
Weight $2$
Character orbit 136.n
Rep. character $\chi_{136}(9,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $20$
Newform subspaces $3$
Sturm bound $36$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 136.n (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 88 20 68
Cusp forms 56 20 36
Eisenstein series 32 0 32

Trace form

\( 20 q - 12 q^{9} + O(q^{10}) \) \( 20 q - 12 q^{9} + 4 q^{11} + 8 q^{17} - 16 q^{25} + 12 q^{27} - 16 q^{29} - 16 q^{31} - 64 q^{35} - 16 q^{39} - 16 q^{41} + 4 q^{43} - 40 q^{45} + 8 q^{49} + 24 q^{53} + 52 q^{59} + 24 q^{61} + 96 q^{63} + 8 q^{65} - 24 q^{67} + 80 q^{69} + 24 q^{71} + 16 q^{73} + 100 q^{75} + 40 q^{79} + 20 q^{83} + 24 q^{85} - 96 q^{87} - 16 q^{91} - 80 q^{93} - 8 q^{95} - 52 q^{97} - 72 q^{99} + O(q^{100}) \)

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.n.a 136.n 17.d $4$ $1.086$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1-\zeta_{8})q^{3}+(1-\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)
136.2.n.b 136.n 17.d $4$ $1.086$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1+\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}+\cdots)q^{5}+\cdots\)
136.2.n.c 136.n 17.d $12$ $1.086$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{2}q^{3}+\beta _{8}q^{5}+(1-\beta _{3}-\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(136, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)