Space of modular forms of level 144, weight 3, and Character 144.m

• Label: 144.3.m
• Level: $144$
• Weight: $3$
• Character orbit: 144.m
• Rep. character: $\chi_{144}(19,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $38$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	104	42	62
Cusp forms	88	38	50
Eisenstein series	16	4	12

Trace form

38 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 8 * q^8 - 4 * q^10 - 14 * q^11 - 2 * q^13 + 32 * q^14 + 24 * q^16 + 4 * q^17 - 34 * q^19 + 4 * q^20 + 84 * q^22 + 68 * q^23 + 4 * q^26 - 64 * q^28 - 14 * q^29 - 168 * q^32 - 4 * q^34 + 4 * q^35 + 46 * q^37 - 208 * q^38 - 224 * q^40 + 14 * q^43 - 108 * q^44 - 60 * q^46 + 178 * q^49 + 190 * q^50 - 212 * q^52 + 82 * q^53 - 260 * q^55 + 392 * q^56 + 280 * q^58 - 78 * q^59 - 34 * q^61 + 420 * q^62 + 112 * q^64 + 20 * q^65 - 162 * q^67 + 336 * q^68 + 344 * q^70 - 252 * q^71 - 256 * q^74 + 148 * q^76 - 12 * q^77 - 784 * q^80 - 16 * q^82 - 158 * q^83 + 108 * q^85 - 796 * q^86 - 440 * q^88 - 4 * q^91 - 328 * q^92 - 744 * q^94 - 4 * q^97 + 430 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.3.m.a	$144$	$3$	144.m	16.f	$4$	$6$	$3$	$3.924$	6.0.399424.1	None					16.3.f.a	$2$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}+(-1-\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
144.3.m.b	$144$	$3$	144.m	16.f	$4$	$16$	$8$	$3.924$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			144.3.m.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{2}+(-1-\beta _{2})q^{4}+\beta _{8}q^{5}+(\beta _{11}+\cdots)q^{7}+\cdots\)
144.3.m.c	$144$	$3$	144.m	16.f	$4$	$16$	$8$	$3.924$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					48.3.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{2}+(1-\beta _{1})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)