Space of modular forms of level 11, weight 33, and Character 11.b

• Label: 11.33.b
• Level: $11$
• Weight: $33$
• Character orbit: 11.b
• Rep. character: $\chi_{11}(10,\cdot)$
• Character field: $\Q$
• Dimension: $31$
• Newform subspaces: $2$
• Sturm bound: $33$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(33\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(11, [\chi])\).

	Total	New	Old
Modular forms	33	33	0
Cusp forms	31	31	0
Eisenstein series	2	2	0

Trace form

31 * q + 44170411 * q^3 - 70314668348 * q^4 + 204484372543 * q^5 + 23695618292427790 * q^9 + 99464988303759419 * q^11 + 179571698325659236 * q^12 - 939077756652939624 * q^14 - 347136535576270399 * q^15 + 106321434165888974920 * q^16 - 1254096636518247394772 * q^20 - 12451846300895917208040 * q^22 - 16588226474294978174309 * q^23 + 187391650652436613004958 * q^25 - 198890048173606824646296 * q^26 + 203152642992899381240497 * q^27 - 1627844815850982685739797 * q^31 + 1875028609544342529047551 * q^33 + 19555270398271796036103576 * q^34 - 117494289098420966820167216 * q^36 + 3935520892965847636882991 * q^37 - 65197651424756254976547480 * q^38 - 93763023117469493771626440 * q^42 - 374926375484255525950012180 * q^44 - 996166065421355603779192756 * q^45 + 599002291623510473177743126 * q^47 - 4888724798088701747446332824 * q^48 + 1015559621085806698647094447 * q^49 + 13921206977104553967684540526 * q^53 + 20705372240014651223371090523 * q^55 + 8291195501410404410735081328 * q^56 - 10422450169964561500915955520 * q^58 - 38520570054317676851029953221 * q^59 + 224210627312962409308565166716 * q^60 - 48508152487851581129938905392 * q^64 + 436064304585559529257045326120 * q^66 + 16924673018208909826658727851 * q^67 - 491860002491719180448206100419 * q^69 + 711240398582233539623997104040 * q^70 - 905329990257964919165847842213 * q^71 - 1037504549468697000732672173844 * q^75 - 1978223909794330701038507497680 * q^77 - 9062552392025584323006322293720 * q^78 + 20714946998822227098123088412728 * q^80 + 20197557042397201587218590596397 * q^81 + 17029303290121852007171127565320 * q^82 - 43501887190969107407549210301456 * q^86 + 93966709680584471966426151789840 * q^88 + 19339678547360871782389482176383 * q^89 - 77012766638054049848594862835536 * q^91 + 301266914446289650110031076977156 * q^92 + 113265662860121214104748442267277 * q^93 - 164337666071575656582375491949649 * q^97 + 318756719030527662117345022344742 * q^99

Decomposition of \(S_{33}^{\mathrm{new}}(11, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.33.b.a	$11$	$33$	11.b	11.b	$2$	$1$	$1$	$71.353$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	✓			11.33.b.a	$2$	$0$	\(0\)	\(-85968833\)	\(-9728091649\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-85968833q^{3}+2^{32}q^{4}-9728091649q^{5}+\cdots\)
11.33.b.b	$11$	$33$	11.b	11.b	$2$	$30$	$30$	$71.353$		None		✓	✓		11.33.b.b	$2$	$0$	\(0\)	\(130139244\)	\(214212464192\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$