Properties

Label 144.3.q
Level $144$
Weight $3$
Character orbit 144.q
Rep. character $\chi_{144}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $22$
Newform subspaces $5$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

\( 22 q + 2 q^{3} - 3 q^{5} + q^{7} + 2 q^{9} + 3 q^{11} - q^{13} + 35 q^{15} + 4 q^{19} + 15 q^{21} + 3 q^{23} + 34 q^{25} + 74 q^{27} - 75 q^{29} - 23 q^{31} - 23 q^{33} - 4 q^{37} - 55 q^{39} - 39 q^{41}+ \cdots + 499 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.3.q.a 144.q 9.d $2$ $3.924$ \(\Q(\sqrt{-3}) \) None 9.3.d.a \(0\) \(3\) \(6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(3-3\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
144.3.q.b 144.q 9.d $4$ $3.924$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 36.3.g.a \(0\) \(-3\) \(9\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{3})q^{3}+(4-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
144.3.q.c 144.q 9.d $4$ $3.924$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 18.3.d.a \(0\) \(0\) \(-18\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\beta _{1}-\beta _{3})q^{3}+(-3-3\beta _{1})q^{5}+\cdots\)
144.3.q.d 144.q 9.d $4$ $3.924$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 72.3.m.a \(0\) \(12\) \(6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
144.3.q.e 144.q 9.d $8$ $3.924$ 8.0.\(\cdots\).9 None 72.3.m.b \(0\) \(-10\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)