Space of modular forms of level 44, weight 6, and trivial character

• Label: 44.6.a
• Level: $44$
• Weight: $6$
• Character orbit: 44.a
• Rep. character: $\chi_{44}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	44.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(44))\).

	Total	New	Old
Modular forms	33	3	30
Cusp forms	27	3	24
Eisenstein series	6	0	6

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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(7\)	\(0\)	\(7\)		\(5\)	\(0\)	\(5\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(10\)	\(0\)	\(10\)		\(8\)	\(0\)	\(8\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(8\)	\(2\)	\(6\)		\(7\)	\(2\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(8\)	\(1\)	\(7\)		\(7\)	\(1\)	\(6\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(15\)	\(1\)	\(14\)		\(12\)	\(1\)	\(11\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(18\)	\(2\)	\(16\)		\(15\)	\(2\)	\(13\)		\(3\)	\(0\)	\(3\)

Trace form

3 * q + q^3 - 101 * q^5 + 218 * q^7 + 330 * q^9 - 121 * q^11 + 852 * q^13 + 1497 * q^15 - 1278 * q^17 + 120 * q^19 - 4130 * q^21 + 6937 * q^23 + 1076 * q^25 - 9125 * q^27 + 1456 * q^29 - 447 * q^31 + 1573 * q^33 - 4950 * q^35 - 7695 * q^37 - 11316 * q^39 - 7024 * q^41 + 9142 * q^43 - 2342 * q^45 + 29896 * q^47 - 3081 * q^49 + 38918 * q^51 - 17010 * q^53 - 6897 * q^55 - 49352 * q^57 - 19653 * q^59 + 107284 * q^61 + 97772 * q^63 + 6548 * q^65 - 32169 * q^67 - 43429 * q^69 - 61093 * q^71 - 28204 * q^73 - 15716 * q^75 - 38478 * q^77 - 43318 * q^79 - 46701 * q^81 + 2918 * q^83 + 185778 * q^85 - 1424 * q^87 + 2573 * q^89 + 198968 * q^91 - 396141 * q^93 + 61208 * q^95 + 76363 * q^97 - 86878 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(44))\) 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
44.6.a.a	$44$	$6$	44.a	1.a	$1$	$1$	$1$	$7.057$	\(\Q\)	None	✓	✓	✓	✓	44.6.a.a	$1$	$1$	\(0\)	\(7\)	\(-79\)	\(-50\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+7q^{3}-79q^{5}-50q^{7}-194q^{9}+\cdots\)
44.6.a.b	$44$	$6$	44.a	1.a	$1$	$2$	$2$	$7.057$	\(\Q(\sqrt{31}) \)	None	✓	✓	✓	✓	44.6.a.b	$1$	$0$	\(0\)	\(-6\)	\(-22\)	\(268\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-3+\beta )q^{3}+(-11+2\beta )q^{5}+(134+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(44))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(44)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)