Properties

Label 144.2.s
Level $144$
Weight $2$
Character orbit 144.s
Rep. character $\chi_{144}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $5$
Sturm bound $48$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(48\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(144, [\chi])\).

Total New Old
Modular forms 60 12 48
Cusp forms 36 12 24
Eisenstein series 24 0 24

Trace form

\( 12 q + 6 q^{9} + O(q^{10}) \) \( 12 q + 6 q^{9} - 12 q^{21} + 6 q^{25} - 36 q^{29} - 18 q^{33} - 18 q^{41} - 36 q^{45} + 6 q^{49} + 30 q^{57} + 72 q^{65} + 72 q^{69} - 36 q^{73} + 72 q^{77} + 54 q^{81} - 18 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.2.s.a 144.s 36.h $2$ $1.150$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
144.2.s.b 144.s 36.h $2$ $1.150$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1-\zeta_{6})q^{7}+\cdots\)
144.2.s.c 144.s 36.h $2$ $1.150$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1+\zeta_{6})q^{7}+\cdots\)
144.2.s.d 144.s 36.h $2$ $1.150$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots\)
144.2.s.e 144.s 36.h $4$ $1.150$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}^{3}q^{3}+(1+\zeta_{12})q^{5}+(-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)