Space of modular forms of level 144, weight 2, and Character 144.k

• Label: 144.2.k
• Level: $144$
• Weight: $2$
• Character orbit: 144.k
• Rep. character: $\chi_{144}(37,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $18$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $4$

Defining parameters

Level:	$N$	$=$	$144 = 2^{4} \cdot 3^{2}$
Weight:	$k$	$=$	$2$
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:			$48$
Trace bound:			$4$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(144, [\chi])$.

	Total	New	Old
Modular forms	56	22	34
Cusp forms	40	18	22
Eisenstein series	16	4	12

Trace form

18 * q + 2 * q^2 + 2 * q^5 + 8 * q^8 + 8 * q^10 + 6 * q^11 - 2 * q^13 - 8 * q^14 - 8 * q^16 + 4 * q^17 - 10 * q^19 - 20 * q^20 - 8 * q^22 - 24 * q^26 - 16 * q^28 + 10 * q^29 - 16 * q^31 - 8 * q^32 - 36 * q^34 - 20 * q^35 + 6 * q^37 + 20 * q^38 - 16 * q^40 - 22 * q^43 + 44 * q^44 + 36 * q^46 - 16 * q^47 - 10 * q^49 + 42 * q^50 + 36 * q^52 - 6 * q^53 + 8 * q^56 + 12 * q^58 - 26 * q^59 + 14 * q^61 - 4 * q^62 + 48 * q^64 + 12 * q^65 + 6 * q^67 - 32 * q^68 + 32 * q^70 - 52 * q^74 - 36 * q^76 - 20 * q^77 + 32 * q^79 - 16 * q^80 + 42 * q^83 - 28 * q^85 + 16 * q^86 + 24 * q^88 + 52 * q^91 + 40 * q^92 + 8 * q^94 + 60 * q^95 - 4 * q^97 + 46 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(144, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.2.k.a	$144$	$2$	144.k	16.e	$4$	$2$	$1$	$1.150$	$\Q(\sqrt{-1})$	None					16.2.e.a	$2$	$0$	$2$	$0$	$2$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(i+1)q^{5}+\cdots$
144.2.k.b	$144$	$2$	144.k	16.e	$4$	$8$	$4$	$1.150$	8.0.18939904.2	None					48.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+(-1-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
144.2.k.c	$144$	$2$	144.k	16.e	$4$	$8$	$4$	$1.150$	8.0.629407744.1	None		✓			144.2.k.c	$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{4}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(144, [\chi])$ into lower level spaces

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