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Properties

Label 144.5.o
Level $144$
Weight $5$
Character orbit 144.o
Rep. character $\chi_{144}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $3$
Sturm bound $120$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 144.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(144, [\chi])\).

Total New Old
Modular forms 204 48 156
Cusp forms 180 48 132
Eisenstein series 24 0 24

Trace form

\( 48 q + 168 q^{9} + O(q^{10}) \) \( 48 q + 168 q^{9} + 144 q^{17} - 912 q^{21} - 3000 q^{25} - 1584 q^{29} - 3528 q^{33} + 1656 q^{41} - 4464 q^{45} + 8232 q^{49} + 10080 q^{53} - 7656 q^{57} + 13536 q^{65} - 1440 q^{69} + 10224 q^{73} - 16992 q^{77} - 23112 q^{81} + 42624 q^{89} - 17280 q^{93} - 16920 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.5.o.a 144.o 36.f $16$ $14.885$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 144.5.o.a \(0\) \(-15\) \(-3\) \(39\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{5})q^{3}+\beta _{8}q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
144.5.o.b 144.o 36.f $16$ $14.885$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 144.5.o.b \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{4}q^{3}+(1-\beta _{1}-\beta _{3})q^{5}+(\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
144.5.o.c 144.o 36.f $16$ $14.885$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 144.5.o.a \(0\) \(15\) \(-3\) \(-39\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{5})q^{3}+\beta _{8}q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)