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Properties

Label 156.2.p
Level $156$
Weight $2$
Character orbit 156.p
Rep. character $\chi_{156}(35,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 156.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 156 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

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

\( 48 q - 2 q^{4} + 6 q^{6} - 2 q^{9} + O(q^{10}) \) \( 48 q - 2 q^{4} + 6 q^{6} - 2 q^{9} + 6 q^{10} - 16 q^{12} - 12 q^{13} + 2 q^{16} - 20 q^{18} - 20 q^{21} - 4 q^{22} - 12 q^{24} - 32 q^{25} - 24 q^{28} - 6 q^{30} + 10 q^{33} - 28 q^{34} + 22 q^{36} + 12 q^{37} + 20 q^{40} - 4 q^{42} + 8 q^{45} + 32 q^{46} - 24 q^{48} - 16 q^{49} + 28 q^{52} - 32 q^{54} - 36 q^{57} - 50 q^{58} - 12 q^{60} - 16 q^{61} + 76 q^{64} + 24 q^{66} + 2 q^{69} + 80 q^{70} + 48 q^{72} - 40 q^{73} + 22 q^{78} - 10 q^{81} - 2 q^{82} - 46 q^{84} + 32 q^{85} - 60 q^{88} + 156 q^{90} + 60 q^{93} + 8 q^{94} + 96 q^{96} + 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.p.a 156.p 156.p $8$ $1.246$ 8.0.3317760000.3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{2}-\beta _{6}q^{3}-2\beta _{4}q^{4}+(\beta _{2}-\beta _{7})q^{5}+\cdots\)
156.2.p.b 156.p 156.p $40$ $1.246$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$