Space of modular forms of level 20, weight 37, and Character 20.d

• Label: 20.37.d
• Level: $20$
• Weight: $37$
• Character orbit: 20.d
• Rep. character: $\chi_{20}(19,\cdot)$
• Character field: $\Q$
• Dimension: $106$
• Newform subspaces: $3$
• Sturm bound: $111$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 37 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(111\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(20, [\chi])\).

	Total	New	Old
Modular forms	110	110	0
Cusp forms	106	106	0
Eisenstein series	4	4	0

Trace form

106 * q - 22883429648 * q^4 - 1587598983830 * q^5 - 103618226406352 * q^6 + 5103217600097970110 * q^9 + 1627054447515827040 * q^10 - 1318136183028326256592 * q^14 + 1066508231100404145856 * q^16 - 114525728851215647511920 * q^20 - 563064361691193400740344 * q^21 + 21902347656277502655828608 * q^24 + 7010888447508638267711050 * q^25 - 45497422310541027363164736 * q^26 + 66423277738557525137797364 * q^29 + 593690321214992115318263600 * q^30 + 2806125899660537831632630656 * q^34 - 6356701916735896838835575536 * q^36 + 128291065211131247075090607360 * q^40 - 240257280106466305764492742348 * q^41 - 303591588473830123626765678720 * q^44 - 1206327519265441266887683251970 * q^45 + 3813071685537927874269263225648 * q^46 + 33660189721725397975758100152990 * q^49 - 7929667902603650222881141214400 * q^50 + 22420017002097987930855567806816 * q^54 + 28030515708154456199248236376448 * q^56 + 213333349271325070123043672822400 * q^60 + 253548662678465116589933812033172 * q^61 - 1046893407710549224775945946699008 * q^64 + 171889226215453780069597281313920 * q^65 - 1537997663126204188085397676462080 * q^66 + 3712259647262819542331744764840456 * q^69 - 2332568247907781283804351558562000 * q^70 + 28871525728729179433814663789470656 * q^74 - 7842107536081536186134723803593600 * q^76 + 58717225711270355256855872330067520 * q^80 + 152807454107385009562991317418129522 * q^81 - 231394042934406304293931206532258304 * q^84 - 119731680630319223762088767841035520 * q^85 - 179573409660821088212094437949759952 * q^86 + 86930462496373026640345922857947284 * q^89 + 148809785974144837896480380277363360 * q^90 + 821398770687597869993444134648843568 * q^94 + 757634139946900641041356971011191808 * q^96

Decomposition of \(S_{37}^{\mathrm{new}}(20, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.37.d.a	$20$	$37$	20.d	20.d	$2$	$1$	$1$	$164.183$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	✓			20.37.d.a	$2$	$0$	\(-262144\)	\(652871042\)	\(38\!\cdots\!25\)	\(15\!\cdots\!82\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{18}q^{2}+652871042q^{3}+2^{36}q^{4}+\cdots\)
20.37.d.b	$20$	$37$	20.d	20.d	$2$	$1$	$1$	$164.183$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	✓			20.37.d.a	$2$	$0$	\(262144\)	\(-652871042\)	\(38\!\cdots\!25\)	\(-15\!\cdots\!82\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{18}q^{2}-652871042q^{3}+2^{36}q^{4}+\cdots\)
20.37.d.c	$20$	$37$	20.d	20.d	$2$	$104$	$104$	$164.183$		None		✓	✓		20.37.d.c	$4$	$0$	\(0\)	\(0\)	\(-92\!\cdots\!80\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$