Space of modular forms of level 144, weight 9, and Character 144.q

• Label: 144.9.q
• Level: $144$
• Weight: $9$
• Character orbit: 144.q
• Rep. character: $\chi_{144}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $94$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(144, [\chi])\).

	Total	New	Old
Modular forms	396	98	298
Cusp forms	372	94	278
Eisenstein series	24	4	20

Trace form

94 * q + 2 * q^3 - 3 * q^5 + q^7 - 1906 * q^9 + 3 * q^11 - q^13 + 91907 * q^15 + 4 * q^19 - 164289 * q^21 + 3 * q^23 + 3359374 * q^25 - 1316446 * q^27 - 1897635 * q^29 + 214177 * q^31 - 137939 * q^33 - 4 * q^37 + 6679457 * q^39 - 2063379 * q^41 + 3393985 * q^43 - 3550627 * q^45 + 20714403 * q^47 - 33765264 * q^49 - 6174944 * q^51 + 781254 * q^55 - 9145876 * q^57 + 35302179 * q^59 - q^61 - 79340319 * q^63 + 5224893 * q^65 + q^67 + 16157245 * q^69 + 32396444 * q^73 - 148129982 * q^75 - 35105475 * q^77 + q^79 + 118397678 * q^81 + 105288483 * q^83 + 390624 * q^85 - 206815869 * q^87 - 169039486 * q^91 + 1008767 * q^93 + 476132550 * q^95 - 56298481 * q^97 + 83247043 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.9.q.a	$144$	$9$	144.q	9.d	$6$	$14$	$7$	$58.663$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					9.9.d.a	$2$	$0$	\(0\)	\(93\)	\(438\)	\(-922\)	$2^{14}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(8-3\beta _{2}-\beta _{4}+\beta _{5})q^{3}+(42-21\beta _{2}+\cdots)q^{5}+\cdots\)
144.9.q.b	$144$	$9$	144.q	9.d	$6$	$16$	$8$	$58.663$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					18.9.d.a	$2$	$0$	\(0\)	\(-126\)	\(-882\)	\(1846\)	$2^{32}\cdot 3^{25}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-7-2\beta _{1}+\beta _{2}+\beta _{5})q^{3}+(-73+\cdots)q^{5}+\cdots\)
144.9.q.c	$144$	$9$	144.q	9.d	$6$	$16$	$8$	$58.663$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					36.9.g.a	$2$	$0$	\(0\)	\(-21\)	\(441\)	\(-923\)	$2^{20}\cdot 3^{28}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-7-11\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(37+\cdots)q^{5}+\cdots\)
144.9.q.d	$144$	$9$	144.q	9.d	$6$	$48$	$24$	$58.663$		None			✓		72.9.m.a	$2$	$0$	\(0\)	\(56\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{9}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

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