Space of modular forms of level 22, weight 4, and Character 22.c

• Label: 22.4.c
• Level: $22$
• Weight: $4$
• Character orbit: 22.c
• Rep. character: $\chi_{22}(3,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(22, [\chi])\).

	Total	New	Old
Modular forms	44	12	32
Cusp forms	28	12	16
Eisenstein series	16	0	16

Trace form

12 * q + 2 * q^2 + 2 * q^3 - 12 * q^4 + 8 * q^5 + 42 * q^6 + 24 * q^7 + 8 * q^8 - 145 * q^9 - 104 * q^10 - 111 * q^11 - 72 * q^12 + 98 * q^13 + 52 * q^14 + 224 * q^15 - 48 * q^16 + 184 * q^17 + 304 * q^18 - 213 * q^19 + 32 * q^20 - 280 * q^21 - 22 * q^22 + 404 * q^23 + 168 * q^24 + 109 * q^25 - 12 * q^26 + 245 * q^27 - 104 * q^28 - 392 * q^29 - 396 * q^30 + 96 * q^31 - 128 * q^32 - 1155 * q^33 - 516 * q^34 - 662 * q^35 - 40 * q^36 - 12 * q^37 - 548 * q^38 - 448 * q^39 + 224 * q^40 + 708 * q^41 + 1940 * q^42 + 2602 * q^43 + 1016 * q^44 + 2404 * q^45 - 424 * q^46 - 818 * q^47 + 32 * q^48 - 661 * q^49 + 166 * q^50 - 1579 * q^51 - 408 * q^52 - 526 * q^53 - 2288 * q^54 + 26 * q^55 + 128 * q^56 - 769 * q^57 - 916 * q^58 - 955 * q^59 - 1224 * q^60 + 718 * q^61 + 2020 * q^62 + 1064 * q^63 - 192 * q^64 + 44 * q^65 + 2656 * q^66 + 490 * q^67 + 736 * q^68 - 554 * q^69 + 24 * q^70 - 1550 * q^71 - 824 * q^72 - 1640 * q^73 - 220 * q^74 - 3561 * q^75 - 712 * q^76 + 498 * q^77 - 2320 * q^78 + 748 * q^79 - 512 * q^80 + 3006 * q^81 + 62 * q^82 + 2829 * q^83 + 2400 * q^84 - 148 * q^85 + 2186 * q^86 + 3792 * q^87 + 472 * q^88 - 474 * q^89 + 1640 * q^90 + 4278 * q^91 - 1624 * q^92 + 7052 * q^93 - 1040 * q^94 - 720 * q^95 - 128 * q^96 - 3109 * q^97 - 4776 * q^98 - 7867 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(22, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
22.4.c.a	$22$	$4$	22.c	11.c	$5$	$4$	$1$	$1.298$	\(\Q(\zeta_{10})\)	None		✓			22.4.c.a	$2$	$0$	\(-2\)	\(-1\)	\(3\)	\(25\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-2\zeta_{10}q^{2}+(-3+3\zeta_{10}+8\zeta_{10}^{3})q^{3}+\cdots\)
22.4.c.b	$22$	$4$	22.c	11.c	$5$	$8$	$2$	$1.298$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓		22.4.c.b	$2$	$0$	\(4\)	\(3\)	\(5\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-2\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(22, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)