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Properties

Label 136.2.k
Level $136$
Weight $2$
Character orbit 136.k
Rep. character $\chi_{136}(81,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $4$
Sturm bound $36$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 136.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 44 8 36
Cusp forms 28 8 20
Eisenstein series 16 0 16

Trace form

\( 8 q + 2 q^{3} - 2 q^{5} + O(q^{10}) \) \( 8 q + 2 q^{3} - 2 q^{5} - 2 q^{11} + 4 q^{13} - 6 q^{17} + 16 q^{21} - 12 q^{23} - 16 q^{27} + 2 q^{29} - 8 q^{31} - 28 q^{33} + 40 q^{35} - 30 q^{37} - 20 q^{39} - 8 q^{41} + 10 q^{45} - 10 q^{51} + 32 q^{57} + 2 q^{61} + 24 q^{63} + 8 q^{65} + 52 q^{67} + 8 q^{69} - 4 q^{71} - 4 q^{73} + 50 q^{75} + 12 q^{79} + 28 q^{81} - 30 q^{85} + 8 q^{89} - 24 q^{91} - 64 q^{95} + 32 q^{97} - 22 q^{99} + O(q^{100}) \)

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.k.a 136.k 17.c $2$ $1.086$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(-3-3i)q^{5}+(-3+\cdots)q^{7}+\cdots\)
136.2.k.b 136.k 17.c $2$ $1.086$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(2+2i)q^{5}+(2-2i)q^{7}+\cdots\)
136.2.k.c 136.k 17.c $2$ $1.086$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1+i)q^{5}+(-1+i)q^{7}+\cdots\)
136.2.k.d 136.k 17.c $2$ $1.086$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{3}+(-1-i)q^{5}+(2-2i)q^{7}+\cdots\)

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

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