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

• Label: 55.4.b
• Level: $55$
• Weight: $4$
• Character orbit: 55.b
• Rep. character: $\chi_{55}(34,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	55.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
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	20	16	4
Cusp forms	16	16	0
Eisenstein series	4	0	4

Trace form

16 * q - 60 * q^4 + 10 * q^5 + 4 * q^6 - 176 * q^9 + 62 * q^10 + 44 * q^11 - 16 * q^14 - 26 * q^15 + 360 * q^16 + 168 * q^19 - 116 * q^20 - 176 * q^21 - 200 * q^24 - 126 * q^25 + 36 * q^26 + 552 * q^29 - 950 * q^30 + 728 * q^31 + 72 * q^34 + 252 * q^35 + 912 * q^36 + 944 * q^39 - 1644 * q^40 - 408 * q^41 - 748 * q^44 - 220 * q^45 + 876 * q^46 - 1484 * q^49 - 214 * q^50 + 72 * q^51 - 2292 * q^54 + 198 * q^55 + 2496 * q^56 - 276 * q^59 + 1804 * q^60 - 560 * q^61 - 1900 * q^64 + 1864 * q^65 + 528 * q^66 - 3196 * q^69 - 2152 * q^70 - 768 * q^71 + 5108 * q^74 + 1614 * q^75 + 1832 * q^76 + 1240 * q^79 + 2384 * q^80 - 200 * q^81 + 5160 * q^84 - 684 * q^85 - 4396 * q^86 - 2104 * q^89 - 3064 * q^90 + 3384 * q^91 + 2200 * q^94 - 4584 * q^95 - 9208 * q^96 - 1408 * q^99

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.b.a	$55$	$4$	55.b	5.b	$2$	$6$	$6$	$3.245$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓			55.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
55.4.b.b	$55$	$4$	55.b	5.b	$2$	$10$	$10$	$3.245$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		55.4.b.b	$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{3}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-6+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)