Space of modular forms of level 11, weight 35, and Character 11.b

• Label: 11.35.b
• Level: $11$
• Weight: $35$
• Character orbit: 11.b
• Rep. character: $\chi_{11}(10,\cdot)$
• Character field: $\Q$
• Dimension: $33$
• Newform subspaces: $2$
• Sturm bound: $35$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 35 \)
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:			\(35\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{35}(11, [\chi])\).

	Total	New	Old
Modular forms	35	35	0
Cusp forms	33	33	0
Eisenstein series	2	2	0

Trace form

33 * q - 199244087 * q^3 - 288669770652 * q^4 - 748552995931 * q^5 + 138581449723201342 * q^9 + 360633738940770493 * q^11 + 2807161611289593172 * q^12 - 65110073012269384584 * q^14 - 19858249128062733685 * q^15 + 2652428193984591417384 * q^16 + 20562227573815164656636 * q^20 + 49336404279944127108840 * q^22 + 463824776808172185428873 * q^23 + 2327450848162296859284246 * q^25 + 2040898832205684328902216 * q^26 - 3001224498285076252734581 * q^27 - 25209722909262420390829839 * q^31 - 39277071047393425153866827 * q^33 - 233258103449584973512182504 * q^34 - 161756377844267796683307776 * q^36 - 617229353872591919039456403 * q^37 + 3120793738113732268004622120 * q^38 + 8609538050906862600782171640 * q^42 - 36909481675752240850164375572 * q^44 - 21027606462181498680526677316 * q^45 + 3806646188428269882082269122 * q^47 + 65457024378998930563528473448 * q^48 - 195289938269842825405839175887 * q^49 - 131044360602127642761740385382 * q^53 - 430930984869229808610732285519 * q^55 + 1708743716128029338107788280272 * q^56 + 2522881169638335768452741160480 * q^58 + 7220704037691283695381274733705 * q^59 - 12032036083576245596689426828180 * q^60 - 19968702008612110217199972279696 * q^64 - 23197701453464419713283404684600 * q^66 + 16852817449390768268170135344177 * q^67 + 64462358099879019500849944142519 * q^69 + 136308646546362905307234883247880 * q^70 - 100991353952875491976448933773759 * q^71 + 40235314229020737799903376536260 * q^75 - 140265553637971041991736055671520 * q^77 - 7671223223574681725148479769720 * q^78 - 1180988979368398440490567758875176 * q^80 - 359755947904415861276332131003941 * q^81 - 528002584772914807832715156591480 * q^82 + 2714890583997166496679059623693776 * q^86 + 1915483557085044350956381495329840 * q^88 + 4415831643334584610935616286906285 * q^89 - 4860797098032856928464851071031264 * q^91 - 23237544034460106464501657755892908 * q^92 + 12257703473792644793011153404090191 * q^93 + 16955063545470177102343727360182077 * q^97 - 35897968240749725367176672204546138 * q^99

Decomposition of \(S_{35}^{\mathrm{new}}(11, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.35.b.a	$11$	$35$	11.b	11.b	$2$	$1$	$1$	$80.548$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	✓			11.35.b.a	$2$	$0$	\(0\)	\(222600715\)	\(-15\!\cdots\!01\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+222600715q^{3}+2^{34}q^{4}-1512594730201q^{5}+\cdots\)
11.35.b.b	$11$	$35$	11.b	11.b	$2$	$32$	$32$	$80.548$		None		✓	✓		11.35.b.b	$2$	$0$	\(0\)	\(-421844802\)	\(764041734270\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$