Space of modular forms of level 22, weight 14, and trivial character

• Label: 22.14.a
• Level: $22$
• Weight: $14$
• Character orbit: 22.a
• Rep. character: $\chi_{22}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $4$
• Sturm bound: $42$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(42\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(22))\).

	Total	New	Old
Modular forms	41	9	32
Cusp forms	37	9	28
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	$-$	\(2\)
\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(4\)
Minus space		\(-\)	\(5\)

Trace form

\( 9 q + 64 q^{2} - 260 q^{3} + 36864 q^{4} + 2446 q^{5} - 140032 q^{6} + 911448 q^{7} + 262144 q^{8} + 2573229 q^{9} + O(q^{10}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(22))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	11
22.14.a.a	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	\(\Q(\sqrt{100039}) \)	None	✓	$1$	$1$	\(-128\)	\(-662\)	\(-48566\)	\(404508\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+(-331+\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.b	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	\(\Q(\sqrt{55441}) \)	None	✓	$1$	$0$	\(-128\)	\(1626\)	\(7666\)	\(637048\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+(813-3\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.c	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	\(\Q(\sqrt{45769}) \)	None	✓	$1$	$1$	\(128\)	\(-926\)	\(2914\)	\(-170560\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}+(-463-\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.d	$22$	$14$	22.a	1.a	$1$	$3$	$3$	$23.591$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(192\)	\(-298\)	\(40432\)	\(40452\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}+(-10^{2}-\beta _{1}-\beta _{2})q^{3}+2^{12}q^{4}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)