Space of modular forms of level 44, weight 4, and Character 44.e

• Label: 44.4.e
• Level: $44$
• Weight: $4$
• Character orbit: 44.e
• Rep. character: $\chi_{44}(5,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	44.e (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(44, [\chi])\).

	Total	New	Old
Modular forms	84	12	72
Cusp forms	60	12	48
Eisenstein series	24	0	24

Trace form

12 * q - 4 * q^3 - 4 * q^5 + 6 * q^7 + 47 * q^9 + 39 * q^11 - 10 * q^13 + 74 * q^15 - 56 * q^17 - 141 * q^19 - 304 * q^21 - 388 * q^23 - 203 * q^25 - 331 * q^27 + 772 * q^29 + 882 * q^31 + 981 * q^33 + 412 * q^35 - 192 * q^37 - 154 * q^39 - 180 * q^41 - 2330 * q^43 - 1340 * q^45 + 196 * q^47 - 973 * q^49 + 2969 * q^51 + 2246 * q^53 + 2672 * q^55 + 431 * q^57 - 1099 * q^59 - 470 * q^61 - 2008 * q^63 - 3892 * q^65 - 4394 * q^67 - 1394 * q^69 - 2084 * q^71 + 2824 * q^73 + 4623 * q^75 + 3654 * q^77 + 838 * q^79 + 1518 * q^81 + 789 * q^83 - 2632 * q^85 - 3036 * q^87 - 954 * q^89 + 2460 * q^91 - 808 * q^93 + 4362 * q^95 + 2651 * q^97 + 3563 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(44, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
44.4.e.a	$44$	$4$	44.e	11.c	$5$	$12$	$3$	$2.596$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	44.4.e.a	$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{7}q^{3}+(1+\beta _{1}+3\beta _{2}+3\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(44, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(44, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)