Space of modular forms of level 55, weight 4, and Character 55.e

• Label: 55.4.e
• Level: $55$
• Weight: $4$
• Character orbit: 55.e
• Rep. character: $\chi_{55}(32,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$55 = 5 \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	55.e (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$55$
Character field:			$\Q(i)$
Newform subspaces:			$2$
Sturm bound:			$24$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(55, [\chi])$.

	Total	New	Old
Modular forms	40	40	0
Cusp forms	32	32	0
Eisenstein series	8	8	0

Trace form

32 * q + 12 * q^5 - 40 * q^11 + 120 * q^12 + 156 * q^15 - 272 * q^16 - 256 * q^20 + 240 * q^22 - 516 * q^25 + 656 * q^26 - 300 * q^27 - 440 * q^31 - 400 * q^33 + 1512 * q^36 - 700 * q^37 - 1120 * q^38 + 1400 * q^42 + 1208 * q^45 - 1980 * q^47 + 720 * q^48 - 280 * q^53 + 124 * q^55 - 248 * q^56 + 3320 * q^58 + 4336 * q^60 - 4200 * q^66 - 1080 * q^67 - 2960 * q^70 - 1216 * q^71 - 204 * q^75 + 4500 * q^77 - 4520 * q^78 - 4448 * q^80 + 3480 * q^81 + 3160 * q^82 - 4144 * q^86 + 1560 * q^88 + 2696 * q^91 - 11560 * q^92 - 8180 * q^93 + 6380 * q^97

Decomposition of $S_{4}^{\mathrm{new}}(55, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.4.e.a	$55$	$4$	55.e	55.e	$4$	$4$	$2$	$3.245$	$\Q(i, \sqrt{11})$	$\Q(\sqrt{-11})$		✓			55.4.e.a	$4$	$0$	$0$	$16$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(4+4\beta _{1}+\beta _{2}+\beta _{3})q^{3}-8\beta _{1}q^{4}+\cdots$
55.4.e.b	$55$	$4$	55.e	55.e	$4$	$28$	$14$	$3.245$		None		✓	✓		55.4.e.b	$4$	$0$	$0$	$-16$	$12$	$0$		$\mathrm{SU}(2)[C_{4}]$