Space of modular forms of level 144, weight 4, and Character 144.k

• Label: 144.4.k
• Level: $144$
• Weight: $4$
• Character orbit: 144.k
• Rep. character: $\chi_{144}(37,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $58$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	152	62	90
Cusp forms	136	58	78
Eisenstein series	16	4	12

Trace form

58 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 - 40 * q^8 + 52 * q^10 + 22 * q^11 - 2 * q^13 + 160 * q^14 - 104 * q^16 + 4 * q^17 + 22 * q^19 + 116 * q^20 + 348 * q^22 + 284 * q^26 + 352 * q^28 - 198 * q^29 + 368 * q^31 - 8 * q^32 + 28 * q^34 - 20 * q^35 - 10 * q^37 - 24 * q^38 + 512 * q^40 + 26 * q^43 - 668 * q^44 - 332 * q^46 + 944 * q^47 - 2258 * q^49 - 1434 * q^50 - 1316 * q^52 - 374 * q^53 - 856 * q^56 + 1136 * q^58 - 330 * q^59 - 914 * q^61 + 1076 * q^62 - 2512 * q^64 - 484 * q^65 + 1126 * q^67 + 2448 * q^68 + 808 * q^70 + 3192 * q^74 - 700 * q^76 - 1636 * q^77 + 1248 * q^79 + 1936 * q^80 + 5056 * q^82 - 118 * q^83 - 492 * q^85 - 2052 * q^86 - 248 * q^88 - 268 * q^91 - 5928 * q^92 - 872 * q^94 + 828 * q^95 - 4 * q^97 - 7074 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(144, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.4.k.a	$144$	$4$	144.k	16.e	$4$	$10$	$5$	$8.496$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					16.4.e.a	$2$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)
144.4.k.b	$144$	$4$	144.k	16.e	$4$	$24$	$12$	$8.496$		None					48.4.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
144.4.k.c	$144$	$4$	144.k	16.e	$4$	$24$	$12$	$8.496$		None		✓			144.4.k.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{4}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)