Space of modular forms of level 44, weight 2, and trivial character

• Label: 44.2.a
• Level: $44$
• Weight: $2$
• Character orbit: 44.a
• Rep. character: $\chi_{44}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	44.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(44))\).

	Total	New	Old
Modular forms	9	1	8
Cusp forms	4	1	3
Eisenstein series	5	0	5

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
\(-\)	\(+\)	\(-\)	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(1\)

Trace form

q + q^3 - 3 * q^5 + 2 * q^7 - 2 * q^9 - q^11 - 4 * q^13 - 3 * q^15 + 6 * q^17 + 8 * q^19 + 2 * q^21 - 3 * q^23 + 4 * q^25 - 5 * q^27 + 5 * q^31 - q^33 - 6 * q^35 - q^37 - 4 * q^39 - 10 * q^43 + 6 * q^45 - 3 * q^49 + 6 * q^51 - 6 * q^53 + 3 * q^55 + 8 * q^57 + 3 * q^59 - 4 * q^61 - 4 * q^63 + 12 * q^65 - q^67 - 3 * q^69 + 15 * q^71 - 4 * q^73 + 4 * q^75 - 2 * q^77 + 2 * q^79 + q^81 + 6 * q^83 - 18 * q^85 - 9 * q^89 - 8 * q^91 + 5 * q^93 - 24 * q^95 - 7 * q^97 + 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(44))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	11
44.2.a.a	$44$	$2$	44.a	1.a	$1$	$1$	$1$	$0.351$	\(\Q\)	None	✓	✓	✓	✓	44.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(44))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(44)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)