Space of modular forms of level 40, weight 11, and Character 40.e

• Label: 40.11.e
• Level: $40$
• Weight: $11$
• Character orbit: 40.e
• Rep. character: $\chi_{40}(19,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $3$
• Sturm bound: $66$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	40.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(66\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(40, [\chi])\).

	Total	New	Old
Modular forms	62	62	0
Cusp forms	58	58	0
Eisenstein series	4	4	0

Trace form

58 * q - 612 * q^4 + 4476 * q^6 - 1062886 * q^9 - 234040 * q^10 - 4 * q^11 - 1563020 * q^14 - 1501992 * q^16 - 5107044 * q^19 + 7209620 * q^20 - 16455824 * q^24 + 738490 * q^25 + 33760120 * q^26 + 49545460 * q^30 - 68505224 * q^34 + 14674460 * q^35 - 151433516 * q^36 + 20283360 * q^40 + 51872196 * q^41 - 146805544 * q^44 + 71880620 * q^46 + 1856265918 * q^49 + 316622680 * q^50 - 372972928 * q^51 - 925320928 * q^54 - 2661898080 * q^56 - 749542724 * q^59 - 1039147800 * q^60 + 723485088 * q^64 + 1868697060 * q^65 - 1687150328 * q^66 - 1069527580 * q^70 - 5029750320 * q^74 + 11676445760 * q^75 + 2128353096 * q^76 + 8776500200 * q^80 + 19070002410 * q^81 - 4953383800 * q^84 + 3761327596 * q^86 - 8491615244 * q^89 - 628539040 * q^90 - 7808967560 * q^91 - 27470628420 * q^94 - 35945869424 * q^96 + 14125291228 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(40, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
40.11.e.a	$40$	$11$	40.e	40.e	$2$	$1$	$1$	$25.414$	\(\Q\)	\(\Q(\sqrt{-10}) \)	✓	✓			40.11.e.a	$2$	$0$	\(-32\)	\(0\)	\(3125\)	\(26886\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}+2^{10}q^{4}+5^{5}q^{5}+26886q^{7}+\cdots\)
40.11.e.b	$40$	$11$	40.e	40.e	$2$	$1$	$1$	$25.414$	\(\Q\)	\(\Q(\sqrt{-10}) \)	✓	✓			40.11.e.a	$2$	$0$	\(32\)	\(0\)	\(-3125\)	\(-26886\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{5}q^{2}+2^{10}q^{4}-5^{5}q^{5}-26886q^{7}+\cdots\)
40.11.e.c	$40$	$11$	40.e	40.e	$2$	$56$	$56$	$25.414$		None		✓	✓		40.11.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$