Properties

Label 156.2.q
Level $156$
Weight $2$
Character orbit 156.q
Rep. character $\chi_{156}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 156.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
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 68 6 62
Cusp forms 44 6 38
Eisenstein series 24 0 24

Trace form

\( 6 q - q^{3} + 3 q^{7} - 3 q^{9} + O(q^{10}) \) \( 6 q - q^{3} + 3 q^{7} - 3 q^{9} + 18 q^{11} + q^{13} + 6 q^{15} - 2 q^{17} - 18 q^{19} - 2 q^{23} - 22 q^{25} + 2 q^{27} - 4 q^{29} - 6 q^{33} - 14 q^{35} + 6 q^{37} - 10 q^{39} - 6 q^{41} + 11 q^{43} + 14 q^{49} - 8 q^{51} - 36 q^{53} + 6 q^{59} + q^{61} - 3 q^{63} + 52 q^{65} + 21 q^{67} + 10 q^{69} + 6 q^{71} + 15 q^{75} + 12 q^{77} + 14 q^{79} - 3 q^{81} - 54 q^{85} + 14 q^{87} + 12 q^{89} - 7 q^{91} + 15 q^{93} + 39 q^{97} + O(q^{100}) \)

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.q.a 156.q 13.e $2$ $1.246$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(4-2\zeta_{6})q^{7}+\cdots\)
156.2.q.b 156.q 13.e $4$ $1.246$ \(\Q(\sqrt{-3}, \sqrt{-43})\) None \(0\) \(-2\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)