Properties

Label 144.4.i
Level $144$
Weight $4$
Character orbit 144.i
Rep. character $\chi_{144}(49,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $34$
Newform subspaces $6$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 144.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(144, [\chi])\).

Total New Old
Modular forms 156 38 118
Cusp forms 132 34 98
Eisenstein series 24 4 20

Trace form

\( 34 q + 2 q^{3} - q^{5} + q^{7} + 8 q^{9} + O(q^{10}) \) \( 34 q + 2 q^{3} - q^{5} + q^{7} + 8 q^{9} - 65 q^{11} - q^{13} - 19 q^{15} - 80 q^{17} + 4 q^{19} + 93 q^{21} + 139 q^{23} - 326 q^{25} - 376 q^{27} + 27 q^{29} - 89 q^{31} + 7 q^{33} + 594 q^{35} - 4 q^{37} + 377 q^{39} + 9 q^{41} + 127 q^{43} + 563 q^{45} - 111 q^{47} - 540 q^{49} + 562 q^{51} - 4 q^{53} - 246 q^{55} + 1010 q^{57} - 551 q^{59} - q^{61} - 1167 q^{63} + 17 q^{65} + q^{67} - 1523 q^{69} - 232 q^{71} + 824 q^{73} - 914 q^{75} + 357 q^{77} + q^{79} + 224 q^{81} - 883 q^{83} - 126 q^{85} + 1047 q^{87} + 1452 q^{89} - 2662 q^{91} - 1099 q^{93} + 764 q^{95} + 17 q^{97} + 3745 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.4.i.a 144.i 9.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None 18.4.c.a \(0\) \(0\) \(9\) \(-31\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-6\zeta_{6})q^{3}+9\zeta_{6}q^{5}+(-31+31\zeta_{6})q^{7}+\cdots\)
144.4.i.b 144.i 9.c $4$ $8.496$ \(\Q(\sqrt{-3}, \sqrt{-35})\) None 18.4.c.b \(0\) \(-3\) \(9\) \(19\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+(6+6\beta _{1}+3\beta _{3})q^{5}+\cdots\)
144.4.i.c 144.i 9.c $4$ $8.496$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 9.4.c.a \(0\) \(3\) \(-15\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-8+7\beta _{1}+\cdots)q^{5}+\cdots\)
144.4.i.d 144.i 9.c $6$ $8.496$ 6.0.6831243.2 None 36.4.e.a \(0\) \(3\) \(6\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{3}+(-2+3\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
144.4.i.e 144.i 9.c $8$ $8.496$ 8.0.5206055409.1 None 72.4.i.a \(0\) \(3\) \(-5\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{3}+(2\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots\)
144.4.i.f 144.i 9.c $10$ $8.496$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 72.4.i.b \(0\) \(-4\) \(-5\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{8})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

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