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Properties

Label 144.3.o
Level $144$
Weight $3$
Character orbit 144.o
Rep. character $\chi_{144}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $3$
Sturm bound $72$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
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: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(144, [\chi])\).

Total New Old
Modular forms 108 24 84
Cusp forms 84 24 60
Eisenstein series 24 0 24

Trace form

\( 24 q - 12 q^{9} + O(q^{10}) \) \( 24 q - 12 q^{9} + 72 q^{17} + 24 q^{21} - 60 q^{25} + 72 q^{29} - 36 q^{33} - 36 q^{41} - 216 q^{45} + 84 q^{49} - 144 q^{53} - 276 q^{57} - 144 q^{65} - 144 q^{69} - 72 q^{73} + 144 q^{77} + 540 q^{81} + 576 q^{89} + 576 q^{93} + 180 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.3.o.a 144.o 36.f $8$ $3.924$ 8.0.856615824.2 None \(0\) \(-3\) \(3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
144.3.o.b 144.o 36.f $8$ $3.924$ 8.0.121550625.1 None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{1}-\beta _{7})q^{5}+\cdots\)
144.3.o.c 144.o 36.f $8$ $3.924$ 8.0.856615824.2 None \(0\) \(3\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}+\beta _{4})q^{3}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

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