Properties

Label 156.2.r
Level $156$
Weight $2$
Character orbit 156.r
Rep. character $\chi_{156}(23,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $3$
Sturm bound $56$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 156.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 156 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(156, [\chi])\).

Total New Old
Modular forms 64 64 0
Cusp forms 48 48 0
Eisenstein series 16 16 0

Trace form

\( 48 q - 2 q^{4} - 12 q^{6} - 2 q^{9} + O(q^{10}) \) \( 48 q - 2 q^{4} - 12 q^{6} - 2 q^{9} - 10 q^{10} - 4 q^{12} - 4 q^{13} + 2 q^{16} - 8 q^{22} - 18 q^{24} + 12 q^{28} - 24 q^{30} - 6 q^{33} - 14 q^{36} - 36 q^{37} - 60 q^{40} + 16 q^{42} - 36 q^{45} + 24 q^{46} - 10 q^{48} - 16 q^{49} + 52 q^{52} + 30 q^{54} + 54 q^{58} - 8 q^{61} + 28 q^{64} - 56 q^{66} + 18 q^{69} + 12 q^{72} + 62 q^{78} + 6 q^{81} + 58 q^{82} + 126 q^{84} - 72 q^{85} + 48 q^{88} + 52 q^{90} - 56 q^{94} - 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(156, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
156.2.r.a 156.r 156.r $4$ $1.246$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
156.2.r.b 156.r 156.r $4$ $1.246$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{3}+2q^{4}-2\beta _{3}q^{5}+\cdots\)
156.2.r.c 156.r 156.r $40$ $1.246$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$