Space of modular forms of level 22, weight 10, and Character 22.c

• Label: 22.10.c
• Level: $22$
• Weight: $10$
• Character orbit: 22.c
• Rep. character: $\chi_{22}(3,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(30\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(22, [\chi])\).

	Total	New	Old
Modular forms	116	36	80
Cusp forms	100	36	64
Eisenstein series	16	0	16

Trace form

\( 36 q - 16 q^{2} + 2 q^{3} - 2304 q^{4} - 456 q^{5} - 7152 q^{6} + 21192 q^{7} - 4096 q^{8} - 19963 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
22.10.c.a	$22$	$10$	22.c	11.c	$5$	$16$	$4$	$11.331$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(64\)	\(-13\)	\(1999\)	\(3779\)	$2^{12}\cdot 3^{4}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2^{4}+2^{4}\beta _{1}+2^{4}\beta _{2}-2^{4}\beta _{3})q^{2}+\cdots\)
22.10.c.b	$22$	$10$	22.c	11.c	$5$	$20$	$5$	$11.331$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-80\)	\(15\)	\(-2455\)	\(17413\)	$2^{16}\cdot 3^{4}\cdot 5\cdot 11^{7}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2^{4}+2^{4}\beta _{3}-2^{4}\beta _{4}-2^{4}\beta _{5})q^{2}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)